Fully explain $($a$)(5$ points$)$ Apply Simpson's rule to estimate the integral ${\displaystyle \underset{-5}{\overset{3}{}}}f(x)dx$ using four intervals $($i$.$e$,$ find $S_4),$ where the graph of $f(x)$ is given below.

$($b$)(5$ points$)$ Apply the midpoint rule to estimate the integral ${\displaystyle \underset{-3}{\overset{9}{}}}f(x)dx$ using three intervals $($i$.$e$,$ find $M_3),$ where the graph of $f(x)$ is given below.