Riemann Sum

Let a Closed Interval be partitioned by points , the lengths of the resulting intervals between the points are denoted , , ..., . Then the quantity

is called a Riemann sum for a given function and partition. The value is called the Mesh Size of the partition. If the Limit exists, this limit is known as the Riemann Integral of over the interval . The shaded areas in the above plots show the Lower and Upper Sums for a constant Mesh Size.