I always assumed that being honest was a moral component to form integrity.
For example, if your values were 1) To never litter 2) Always be honest 3) Never complain etc - and then you dropped a piece of rubbish on the floor, you lose some integrity. Then you tell your boss you're feeling sick, you're not sick, you lose some integrity. You moan about your work hours, you lose some integrity.
And that to have a great deal integrity means you follow your morals/values as closely as you can.
The issue being, the morals and values which we choose will need to have a social or personal gain. Someone with a belief that causing harm to others is good cannot gain a great deal of integrity...Or maybe they can, and integrity can be segregated into catogories of good and bad.
