Chapter 5.2, Problem 31E

Net area and definite integrals Use geometry (not Riemann sums) to evaluate the following definite integrals. Sketch a graph of the integrand, show the region in question, and interpret your result.

31. ${\displaystyle {\int }_0^{4}f(x)dx}$, where $\begin{array}{ll}f(x)=\{\begin{array}{l}5\hfill \\ 3x-1\hfill \end{array}\hfill & \begin{array}{l}\text{if}x\le 2\hfill \\ \text{if}x>2\hfill \end{array}\hfill \end{array}$