Consider the function $f(x)=x^2-2x.$

a$.$ Using $4$ rectangles and right endpoints, approximate the area between the graph of $y=f(x)$ and the $x-$axis over the interval $0,4$

b$.$ Illustrate your approximation from $($a$)$ with the aide of a graphing calculator if necessary.

c$.$ Improve your approximation from step $($a$)$ by using $8$ rectangles.

d$.$ Using right endpoints and the limit of a Riemann sum, compute the exact area of the region described in $($a$).$