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According to http://integrals.wolfram.com, the answer is (1/2) (sin x cos x).

I believe these integrals are calculated by converting the sine or cosine square with some trigonometric identity first. See this reference: http://en.wikipedia.org/wiki/Trigonometric_identity#Power-reduction_formulas

In this case, the relevant formula is cos2x = (1 + cos 2x) / 2.

According to Mathcad the answer is (1/2)*(sin(x)*cos(x)+x). The proof by derivation confirms this solution.

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Q: How to integrate Cosine to the power of 2?
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