Chapter 5.3, Problem 53E

Think About It Consider a function f that is continuous on the interval [-5, 5] and for which ${\displaystyle {\int }_0^{5}f\left(x\right)dx=4}$

Evaluate each integral.

(a) ${\displaystyle {\int }_0^5\left[f\left(x\right)+2\right]dx}$

(b) ${\displaystyle {\int }_{-2}^{3}f\left(x+2\right)dx}$

(c) ${\displaystyle {\int }_{-5}^{5}f\left(x\right)dx,f\text{is}\text{even}}$

(d) ${\displaystyle {\int }_{-5}^{5}f\left(x\right)dx,f\text{is}\text{odd}}$