If anyone is not clear for (b)

cos(-x) = cos x, so -xcos(-x) = -xcosx, making xcosx an odd function. So, integral from $-\pi$ to 0 will be negative of the integral from 0 to $\pi$ making the sum 0.

cos(-x) = cos x, so -xcos(-x) = -xcosx, making xcosx an odd function. So, integral from $-\pi$ to 0 will be negative of the integral from 0 to $\pi$ making the sum 0.