Unanswered Definite Integration Questions

\hspace{-16}(1)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\sin (kx)\right)^2dx}$\\\\\\ $(2)\;\; \bf{\int_{-\pi}^{\pi}\left(\sum_{k=1}^{2013}\cos (kx)\right)^2dx}$\\\\\\ ...

consider the integrals *Image* let I be the greatest among them. prove that I=I4 ...

{} is fractional func [] is GIF | |is mod *Image* 5. ∫(0 to x)ex-[x]d{x} 6. ∫(0 to 4){ x }dx 7.∫(-5 to 5)min({x+1},{x-1})dx ...