Given the partition $\{0,\frac{\pi}{2},\,\pi\}$, find $L(P)$ and $U(P)$ for the integral $\int_0^{\pi}\sin(x)\,dx$.

Problem: 

Given the partition $\{0,\frac{\pi}{2},\,\pi\}$, find $L(P)$ and $U(P)$ for the integral $\int_0^{\pi}\sin(x)\,dx$.

Answer: 

$L(P)=0$ and $U(P)=\pi$