Given the functions, $f(x)=(x-2{)}^{2}3$ and $g(x)=x3,$ answer each of the following, a ram. $-$

a$)$ Sketch a graph for both functions and clearly label the points of intersection. This should be a noncatculator generated graph.

b$)$ Write and solve an integral expression to represent the area between the functions.

c$)$ Write a limit expression of Reimann sums to represent the integral expression from part b$.$

d$)$ Determine the volume for the region bounded by $f(x)$ and $g(x)$ rotated about the line $x=1.$

e$)$ Write an expression to represent the volume for the region bounded by $f(x)$ and $g(x)$ rotated around the line $x=-1.$