Answer
$F^{'}(x)=\frac{x^{2}}{x^{2}+1}$
Work Step by Step
$F(x)=\int_{1}^{x}(\frac{t^{2}}{t^{2}+1})$
$F^{'}(x)=\frac{d}{dx}\int_{1}^{x}(\frac{t^{2}}{t^{2}+1})$
$=(\frac{x^{2}}{x^{2}+1})$
This is valid since the function $f(t)=(\frac{t^{2}}{t^{2}+1})$ is a continuous function over the implied domain, $\mathbb{R}$
