The rectangles in the graph below illustrate a left endpoint Riemann sum for on the interval .
The value of this left endpoint Riemann sum is
,
and this Riemann sum is
the area
of the region enclosed by , the xaxis, and
the vertical lines x = 3 and x = 7.

Left endpoint Riemann sum for on 
The rectangles in the graph below illustrate a right endpoint Riemann sum for on the interval .
The value of this right endpoint Riemann sum is
,
and this Riemann sum is
the area of the region enclosed by , the xaxis, and the vertical lines x = 3 and x = 7.

Right endpoint Riemann sum for on 