Integrity means to be genuine and open about decisions and actions. It is about what is professed and demonstrated through behavior and action in all dealings and situations.
Integrity is the cornerstone to generate trust. Like trust, people must earn it. Until it is earned, a leader will have a hard time performing, if at all. Covey and the Merrills agree, noting further that it involves dogged determination to achieve a goal. It also involves an open relationship. 
One of the hallmarks of a leader is that he or she exhibit integrity in everything done, whether at work or somewhere else. Leaders exhibit integrity in private and public, observe Kouzes and Posner, and base it on a set of values for making consistent choices under different situations.  These values are the ingredients for a leader to act with integrity, even when facing tremendous costs and risks.
In a very significant way, integrity has three parts to it: emotional honesty, practical intuition, and applied integrity. Emotional honesty requires a serious consideration of instinct or gut feelings. Practical intuition means to have an innate feeling about doing what is right. Applied integrity means to have the courage to take action in accord with emotional honesty and practical intuition. 
Essentially, integrity reflects the important "chain" of belief, commitment, action, and results. In other words, believing in what is right and committing to what is right by taking action to achieve results consistent with beliefs. This chain creates the basis for the other two cornerstones of credibility: ethics and trust. It cannot be contrived or faked; it is a fundamental part of a person's character. 
Integrity does not just happen. Project managers must exhibit integrity constantly. A lapse can wreck effectiveness as a credible leader. Fortunately, project managers have some very effective ways to exercise and maintain integrity.
They must consistently exercise integrity. They must demonstrate it on all issues, making no exceptions. If making exceptions, stakeholders can no longer ascertain whether project managers are straightforward. Project managers with integrity, therefore, exercise it "on and off the field"; their actions are in concert with their beliefs at work and at home. Failure to have consistency will likely permeate actions on a project and credibility will quickly be hurt or destroyed .
Project managers must be reliable; they must follow through. They say something and demonstrate it through action. They do not make impossible promises or fail to keep them, but rather deliver to the expectations they set. Establishing and maintaining credibility allows for no exceptions.
They must act consistently with expectations set and held by others. Project managers function in a role with certain expectations that they and others have. These role expectations are very similar to those that Henry Mintzberg identifies for managers in general. He identifies three roles that managers assume: interpersonal, which includes performing as the leader and liaison of the group ; informational, acting as a spokesperson and disseminating information; and decisional, allocating resources and negotiating.  If they fail to meet expectations with these roles, project managers may find themselves losing credibility.
Project managers must act consistently with their professed beliefs. They should understand the chain discussed earlier: beliefs, commitment, action, and results. If a discontinuity occurs between beliefs and results, people will not know what to expect because they are unpredictable. In other words, alignment must exist from thought through results; otherwise , no one will take a project manager seriously.
They must communicate openly. Project managers must avoid being a spin master or others will be spin masters with them.
Two major challenges, which make open communication difficult, occur on projects that cause project managers to become spin masters. The first challenge is the desire to get along. This desire for acceptance can cause people to become experts at "coloring" information to avoid upsetting others. The other challenge is the desire to want to please the customer. While it is good to focus on a customer, this desire can generate a strong belief that not pleasing a customer will mean the project is a "failure." Naturally, people with such desires will reluctantly communicate openly with the customers or even managers, thereby providing disinformation and misinformation .
Project managers should strive for objectivity. Although strict objectivity is unattainable, they should identify facts and data as much as possible and use both as a means to assess situations. Facts and data, as opposed to assumptions and perceptions, allow project managers and others to base their evaluations and actions on what is right. If project managers lose even the perception of objectivity, however, people will accuse them of being unfair and displaying favoritism. People will be less inclined to condemn project managers over an error in judgment than over an error of intent.
They must be open and approachable, so people are willing and wanting to communicate on just about anything with them. This communication should include negative and positive information. Too often, project managers hear only what they want to hear, or selectively hear. When that occurs, people and project managers often sacrifice integrity. Project managers can best obtain openness by meeting with stakeholders frequently either in a group or one-on-one basis. During meetings, they can obtain openness by encouraging tolerance for diverse ideas or comments different from their own.
Project managers must be honest in all dealings. They must "tell it like it is," the negative as well as the positive. They should also expect the same of stakeholders. Only through honesty can anyone better understand the efficiency and, more importantly, the effectiveness of their projects. Failure to deal honestly, on small and large scales , can result in a serious credibility gap.
They must follow and apply consistently a personal set of beliefs and values. That is, they must demonstrate continuity from idea to results. If results diverge from espoused beliefs, their credibility can crash and recovery will be very difficult. Stephen Covey stresses the need, therefore, for leaders to establish ethical standards to guide their actions. 
Beliefs and values are extremely valuable for project managers who face ambiguous situations. They serve as a "compass" to guide project managers to make the right decisions. They also give people the necessary confidence in their project managers because predictability is reflected in their behavior.
 Stephen R. Covey, A. Roger Merrill, and Rebecca R. Merrill, First Things First , Simon & Schuster, New York, 1994, p. 146.
 James M. Kouzes and Barry Z. Posner, The Leadership Challenge , Jossey-Bass, San Francisco, 1987, p. 301.
 Robert K. Cooper and Ayman Sawaf, Executive EQ , Audio-Tech Business Book Summaries, Willowbrook, IL, November 1997, pp. 2 “9 (Booklet).
 Stephen R. Covey, A. Roger Merrill, and Rebecca R. Merrill, First Things First , Simon & Schuster, New York, 1994, p. 204.
 Henry Mintzberg, The manager's job: folklore and fact, Harvard Business Review , pp. 54 “59, July-August 1975.
 Stephen R. Covey, The Seven Habits of Highly Effective People , Simon & Schuster, New York, 1990, p. 300.