Solution
= Solution
Holding $x$ fixed when taking the <antiderivative> with respect to $t$ gives
$$
h(x)=[x^2t^2-x\cos t]_x^{\pi x^2}=\pi^2x^6-x^4-x\cos(\pi x^2)+x\cos x.
$$
Use the <product rule> and the <chain rule> to differentiate this explicit expression:
$$
\boxed{h'(x)=6\pi^2x^5-4x^3-\cos(\pi x^2)+2\pi x^2\sin(\pi x^2)+\cos x-x\sin x.}
$$
This agrees term by term with part (i).