Derivative of Fresnel integral function with functional limits

Question

How do I find a derivative (with respect to $x$) of a Fresnel integral function with functional limits: $$f(x)=\int_{\sin^2(x^2)}^{e^{2x}}\sin(z^2)\,dz.$$

Answer 1

HINT

Recall that in general

$$f(x)=\int_{a(x)}^{b(x)}g(u) \,du\implies f'(x)=g(b(x))\cdot b'(x)-g(a(x))\cdot a'(x)$$