Answer
$f(4)$=$\frac{\pi}{2}$
Work Step by Step
$x$$\sin (x\pi)$$=$$\textstyle \int\limits_{0}^{x^{2}} f(t)$ $dt$
Take the derivative of both sides
$\sin (x\pi)$$+$$x$$\cos (x\pi)$$\pi$=$2$$f(x^{2})$$x$
Take $x$=$2$
$\sin (2\pi)$$+$$2$$\cos (2\pi)$$\pi$$=$$4$$f(4)$
$0$$+$$2$$\pi$$=$$4$$f(4)$
$\frac{\pi}{2}$$=$$f(4)$
