How to calculate $\int_0^\frac{\pi}{2}(\sin^3x +\cos^3x) \, \mathrm{d}x$? $$\int_0^\frac{\pi}{2}(\sin^3x +\cos^3x) \, \mathrm{d}x$$
How do I compute this? I tried to do the trigonometric manupulation but I can't get the answer.

Hint: $\sin^3 x dx = -\sin^2 xd(\cos x) = (\cos^2 x - 1)d(\cos x)$. Do the same for $\cos^3 x dx$.
