Chapter 7.4, Problem 55E

In Exercises 53–56, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

55. If ${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}f\left(x\right)}dx$ exists, then ${\displaystyle \underset{0}{\overset{\infty }{\int }}f\left(x\right)}dx$ exists, and

${\displaystyle \underset{-\infty }{\overset{\infty }{\int }}f\left(x\right)}dx=2{\displaystyle \underset{0}{\overset{\infty }{\int }}f\left(x\right)}dx$