Integrity means being whole, unbroken, undivided. It describes a person who has united the different parts of his or her personality, so that there is no longer a split in the soul.
For the person of integrity, life may not be easy but it is simple: Figure out what is right and do it. All other considerations come in second.
The rule would be: When facing a dilemma, choose the more morally demanding alternative.
Rabbi Harold Kushner, Living a Life that Matters