Suppose $f$ is a decreasing, concave up$,$ continuous function with values given in the following table:

$\backslash$table$[[x,-1,0,1,2,3,4,5,6,7],[f(x),30,18,8,0,-6,-11,-14,-16,-17]]$

$($a$)(5$ points$)$ Estimate ${\displaystyle \underset{-1}{\overset{5}{}}}f(x)dx$ using $3$ equal$-$width subintervals and left$-$endpoints. Fully simplify your answer.

$($b$)(3$ points$)$ Is your answer above an under$-$estimate or over$-$estimate? What property$($s$)$ of $f$ guarantee this?

$($c$)(4$ points$)$ Let $F(x)$ be an antiderivative of $f(x)$ with $F(5)=100.$ Based on your approximation from $($a$),$ approximate $F(-1).$