Chapter 5.6, Problem 40ES

Determine whether the statement is true or false. Explain your answer.

If $f\left(x\right)$ is continuous everywhere and

$F\left(x\right)={\displaystyle {\int }_0^{x}f\left(t\right)dt}$

then the equation $F\left(x\right)=0$ has at least one solution.