(A) Estimate the area under the graph of
$$f(x) = 2 x^3 + 4$$ from $x = -1$ to $x = 3$, first using 4 approximating rectangles and right endpoints, and then improving your estimate using 8 approximating rectangles and right endpoints.

4 Rectangles =

8 Rectangles =

(B) Repeat part (A) using left endpoints.

4 Rectangles =

8 Rectangles =

(C) Repeat part (A) using midpoints.

4 Rectangles =

8 Rectangles =