Suppose $g$ is continuous on $[2,5]$ and ${\int }_2^5\mid g\left(x\right)\mid dx=0$ Which of the following must be true?

$g\left(x\right)=0$ for all $x\in [2,5]$

$g\left(x\right)$ is positive somewhere on $[2,5]$

$g\left(x\right)$ is negative somewhere on $[2,5]$

$g\left(x\right)$ is not defined at some point in $[2,5]$