As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.
As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.
Answer:
I think is 8.787e+6 cubic inches.
A line parallel to x-axis has 0 slope.
We are given a system of equations,

This will translate into a 2x2 matrix of coefficients (because 2 equations and 2 unknowns),

The matrix will then be applied to the vector (lower dimensions on top),

And the result vector will be whats on the other side of equals sign,

So to put everything together,

Hope this helps :)