Chapter 4.7, Problem 68P

To determine

To prove: If $f$ is continuous on $\left[a,b\right]$ and $u\left(x\right)$ is a differentiable function, then for all $x\in \left[a,b\right],{\displaystyle {\int }_a^{u\left(x\right)}f\left(t\right)dt}=f\left(u\left(x\right)u^{\prime }\left(x\right)\right)$ .