According to "Tables and Integrals, Series, and Products", (Corrected and Enlarged Edition) by Gradshteyn and Ryzhik, paragraph 3.821, integral #9, the definite integral is equal to pi/2.
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I didn't go all the way through the exercise, but it appears that this integral can be solved by making the following substitution: sin^2(x) = 1-cos(2x). and then integrating by parts twice.
Regards,
Kral