Let $g(x)={\displaystyle \underset{0}{\overset{x}{}}}f(t)dt,$ where $f$ is the function whose graph is shown.

$($a$)$ At what values of $x$ do the local maximum and minimum values of $g$ occur?

$x_{\text{m}\text{i}\text{n}}=(smallerx-$value$)$

$x_{\text{m}\text{i}\text{n}}=(largerx-$value$)$

$x_{\text{m}\text{a}\text{x}}=(smallerx-$value$)$

$x_{\text{m}\text{a}\text{x}}=(largerx-$value$)$

$($b$)$ Where does $g$ attain its absolute maximum value?

$x=$

$($c$)$ On what interval is $g$ concave downward? $($Enter your answer using interval notation.$)$