Chapter 5.3, Problem 168E

In the following exercises, use a calculator to estimate the area under the curve by computing $T_{10}$ , the average of the left- and right-endpoint Riemann sums using N = 10 rectangles. Then, using the Fundamental Theorem of Calculus, Part 2, determine the exact area.

168. [T] ${\displaystyle \int \left(\cos x-\sin x\right)dx}$ over $\left[0,\pi \right]$