Given the inequality

(valid for all integers ), generalize the results of Exercise I.4.2 to calculate for any integer .

Using the same method as in the previous two exercise, here and here, we first calculate the lower and upper sums by adding up the areas of the rectangles below and above the curve, respectively.

Then, starting with the given inequality

we multiply each term by to obtain

Following the same method as in the previous exercise we then obtain that if the ordinate at each is given by the area is given by