Chapter 5.3, Problem 1QC

  In Example 1, let B(x) be the area function for f with left endpoint 5. Evaluate B(5) and B(9).

Example 1 Comparing Area Functions

The graph of f is shown in Figure 5.37 with areas of various regions marked. Let $A\left(x\right)={\displaystyle {\int }_{-1}^{x}f\left(t\right)dt}$ and $F\left(x\right)={\displaystyle {\int }_3^{x}f\left(t\right)dt}$ be two area functions for f (note the different left endpoints). Evaluate the following area functions.