Diagram for the Riemann Sum

Question

What is the answer for this? Not the evaluation part but the graph of the Riemann Sum. I originally thought it was the first/top left graph because I thought 'right endpoints' in the question meant the right Riemann sum, but it was the wrong answer.

Can someone please explain?

Answer 1

I assume the graphs to be ordered as :

a b
c d

An area under a curve is the area between the curve and the x axis. In the (a) and (d) graphs, the areas are not between f(x) and the x axis.

That leaves you with (b) and (c). The question specifies that the sample point is chosen as the right endpoint, meaning the bottom / top right corner of the box area is the one that touches the curve, which is the graph (c).