What is a Riemann sum? Why might you want to consider such a sum?

Step 1 of 3:

In this problem, we need to define a Riemann sum and we need to discuss why might you want to consider such a sum.

Step 2 of 3:

Definition:

Riemann sums for a function f defined on , a partition of into a collection of subintervals , and for each , a point , the sum is called a Riemann sum for f determine by the partition