Suppose .
  1. The rectangles in the graph on the left illustrate a left endpoint Riemann sum for on the interval . The value of this left endpoint Riemann sum is and it is an the area of the region enclosed by , the -axis, and the vertical lines and .
  2. The rectangles in the graph on the right illustrate a right endpoint Riemann sum for on the interval . The value of this right endpoint Riemann sum is and it is an the area of the region enclosed by , the -axis, and the vertical lines and .
 
 
Left endpoint Riemann sum   Right endpoint Riemann sum