Estimating the area under the graph

Question

Here is the problem I'm working on:

Estimate the area under the graph of $f(x)=4x^3+6$ 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 = 168

8 Rectangles =

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

4 Rectangles = 56

8 Rectangles =

(C) Repeat part (A) using midpoints.

4 Rectangles = 100

8 Rectangles =

Now I got the three values in there already correct, but the other three I can't figure out what to do. This is how I worked it:

Ive spent at least an hour on this one problem. Thanks!

Answer 1

Why estimate when you could get an exact answer?

$$\int_{-1}^{3}4x^3+6 dx=[x^4+6x]_{-1}^{3}=-5+99=94$$