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.

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1999-05-25