Intellectual integrity, to me, means diligently assessing the ways that your worldview and background and biases affect how you evaluate information. You may never be able to be completely "objective" -- and about some things, you might not want be. But you should aspire to be aware and honest about the effect your position has on your judgment.
I think this is the part that drives me crackers when watching how most "debates" go down on the internet, particularly when people start bringing their evidence into it.