Here are some synonyms of integrity, and none describe what you are describing:
character, decency, goodness, honesty, morality, probity, rectitude, righteousness, rightness, uprightness, virtue, virtuousness
VikingLord wrote: If these guys want to win, then they understand that sometimes you have to take a step backwards to take two forward, and if I were on the team I would have more questions about a coach who guns his star RB for 35 carries to win a meaningless game than I would about a coach who starts throttling his key talent back a bit in that situation with an eye towards next year. What shows greater concern for those veteran players is more a matter of perspective, don't you think, especially in light of the recent injury to AD.
I think showing an appreciation of context is the mark of a coach and GM worth something. I think making those tough calls in tough situations is exactly the kind of medicine this organization needs. Integrity is doing what needs to be done even if it's difficult. I'd say shifting approach to maximize future value in this situation is the definition of integrity.
And like I said - that isn't equivalent to intentionally losing.