True$/$False$.$ If $f$ is integrable on $a,b,$ then there exists a number $x$ in the open interval $(a,b)$ such that

${\displaystyle \underset{a}{\overset{x}{}}}f={\displaystyle \underset{x}{\overset{b}{}}}f$

If your answer is true, then explain your reasoning. If you chose false, then give a counterexample.

$($A$)$ True

$($B$)$ False

$($C$)$ not enough information

$($D$)$ none of the above