There are two parts to this definition. The first has to do with the internal integration of the individual. This is what is at stake in the first part of the definition. Part two is about whether you have the right values and basic beliefs. Consistency is one thing.
Correctness is something else altogether.
The person of integrity doesn't just stick to his convictions, he also has the right convictions. He is plugged into the true moral order of things with genuine moral insight. The ideal person of integrity is at one with the true moral order of things in terms of Knowing Doing Saying Feeling Being. But of course one modern sensibility cries out to know whether there is any such thing as an objective moral order, a transcendent structure of rightness and goodness. It is difficult to examine closely all the world's major religions and philosophies without coming away with the conviction that down deep below all the surface differences, and beneath all the real divergencies, there is at rock bottom a common perception of an objective moral order sensed by all the wisest of people, regardless of their historical period or cultural surroundings.