$2.(20$ Points$)$ Use the plot below to prove that $\backslash ($ f$($c$)($b$-$a$)=$F$($b$)-$F$($a$)\backslash )$ where $\backslash ($ f$($c$)\backslash )$ is the value of the function at the center of your bin and $\backslash ($ b $\backslash )$ and $\backslash ($ a $\backslash )$ bound the functions $(\backslash ($ a$=0$ ; b$=6\backslash )).$ Draw, label, and write out all the equations if you divide the area under the curve into six equal sized rectangles with widths of $1.$

a$.$ What is the area of each of the $6$ rectangles?

b$.$ What is the total area under the curve?

c$.$ How does this estimate compare to your answer in Problem $1$c$?$ Do they match? Should they match?