Chapter 4.5, Problem 62E

If $f$ is continuous function on $ℝ$, prove that ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(x+c\right)}dx={\displaystyle \underset{a+c}{\overset{b+c}{\int }}f\left(x\right)}dx$

For the case where $f\left(x\right)\ge 0$, draw a diagram to intercept this equation geometrically as an equality of areas.