You are right in your definition of Integrity.

Also, principles are not merely a set of ideas or values one must blindly adhere to (no matter how right these ideas appear to be). Principles have to be worked out. People have to develop to reach a principled way of living. In order to get to that principled position, people must have personal integrity (the willingness to act on what they understand is the best position to take). They would not always be right, but they should be true to themselves (true to what they understand is correct). If one continually acts on the best understanding available to them, they are giving up positions they once had for ones they realize are better. The evolving realizations and actions are what developing is about. That is living with integrity.

In that regard I will add, personal integrity is the ability to do what one realizes (through research and/or reason) is the best thing to do. Understanding better and not acting on it leaves one a hypocrite which is worse than doing 'wrong' based on ignorance (naivety).