Question

Explain​ how, in​ general, riemann sum approximations to the area of a region under a curve change as the number of subintervals increases.

Answer 1

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.