The example is somewhat awkward, but I think I know what you're looking for:
Integrity literally means wholeness, and has an implication of honesty and morality. Someone who displays intellectual integrity would be someone whose intellectual works (writings, speeches) were free from dishonesty, shortcuts, plagiarism, etc. It would be someone who never uses faulty logic, and who is admired for making beneficial use of their intelligence.
Opposites of intellectual integrity would be intellectual dishonesty, intellectual laziness, or being intellectually devious.
I would re-write your example as: "The Nobel prizes and other major awards they have garnered over the years are a testament to their intellectual integrity."