A few months ago I learned what is, so far, the most fascinating thing I've learned about human nature: the difference between being right, and being able to look someone in the eyes.
If they practice, people can learn to look you in the eyes even when they're lying to you. But it's kind of like a fake smile; there are involuntary muscles up there. If you know what you're looking for, you can still tell.
But what does it mean if they're looking you in the eyes and they mean it? It means that, at least in that moment, they're doing what they really believe is right. That's the definition of integrity.
That part is easy. That's not the surprising thing.
The surprising thing, to me, was that someone can have integrity and still be completely evil. It's kind of obvious in retrospect; the super-villain in an action movie can always look the hero in the eye, and he always does, just to prove it. He has integrity. Evil with integrity is more respectable, somehow, than plain evil.
All it takes to have integrity is to do what you think is right, no matter how stupid that may be.
Beware of people with integrity.