Let $\displaystyle f(x) = sin x$. Estimate (integral from 0 to pi/2) $\displaystyle \int {f(x)} dx$ by calculating the lower Riemann sums $\displaystyle L(f,P_n)$ and the upper Riemann sums $\displaystyle U(f,P_n)$ for n = 3 with respect to a partition of $\displaystyle P_n$ $\displaystyle [0,\frac{\pi}{2}]$ into n subintervals of equal length. Verify that

$\displaystyle L(f,P_3)<= 1 <= U(f,P_3)$

and explain why $\displaystyle L(f,P_n) <= 1 <= U(f,P_n)$ for all $\displaystyle n > 0$

I don't even know what this means!!