Ted Engstrom gives a succinct definition of integrity:
Simply put, Integrity is doing what you said you would do. It means you keep your promises. When you promised to be faithful to your mate, integrity says you'll stay with that person no matter what - for better or for worse, for richer or for poorer, in sickness and in health. If you promised the Lord that you would give Him the glory, integrity means you keep on doing that whether you're reduced to nothing or exalted to the highest pinnacle on earth. If you promised a friend that you would return a call, integrity means you return it. If you promised your child that you would spend Saturday together, integrity means you keep that appointment. A promise is a holy thing, whether made to a chairman of the board or to a child.