Leibniz integral rule

If $f$ is continuous on $[a,b]$ and $u(x)$ and $v(x)$ are differentiable functions of $x$ whose values lie in $[a,b]$, then $\frac{d}{dx}{\int }_{u(x)}^{v(x)}f(t)dt=f(v(x))\frac{dv}{dx}-f(u(x))\frac{du}{dx}$