Approximate $\displaystyle \int_0^{\pi/2} \sin(x)dx$ by computing $L_f(P)$ and $U_f(P)$, using the partition $\lbrace 0,\pi/6,\pi/4,\pi/3,\pi/2 \rbrace$.

Your answers should be accurate to at least 4 decimal places.
$L_f(P)$ =
$U_f(P)$ =
You may include a formula as an answer.