Answer
$F^{'}(x)=x{\cos {(x)}}$
Work Step by Step
$F(x)=\int_{0}^{x}(t{\cos {(t)}}) {dt}$
$F^{'}(x)=\frac{d}{dx}\int_{0}^{x}(t{\cos {(t)}}) {dt}$
$=x{\cos {(x)}}$
This is valid since the function, $f(t)=t{\cos (t)}$ is a continuous function over the implied domain, $\mathbb{R}$
