Problem with Integral question

[kasse]

If I know that $$\int^{\pi /2}_{0}x^2 cos^2 x dx = \frac{\pi^3}{48} - \frac{pi}{8}$$ can I use this to calculate $$\int^{\pi / 2}_{- \pi /2} u^2 cos^2 u du$$?

 

[arildno]

Obviously, since the integrand is even, the latter integral is just twice the first.