Solve Integral: \int_{-n \pi /2}^{n \pi / 2} y^2[1 + \cos(2y)] dy

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I have the following integral, but I don't know how to solve it: \int_{-n \pi /2}^{n \pi / 2} y^2[1 + \cos(2y)] dy, with n = 1, 3, 5... Any ideas?
 
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Could you distribute the y^2? The first term would just be integral of y^2 and the second you could use Int by parts twice.
 

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