More on Riemann Sums

The rigerous definition of the definite integral uses the term Riemann Sum to mean that:

The difference between this definition and the one used for computation in this chapter is the fact that the partitions in the interval [a,b] do not necessarily have to be equal. In addition, the point within the partition does not necessarily have to be at the midpoint of the partition. The graphic below demonstrates:

As you may surmise, computationally, this definition is more difficult to implement with a computer algebra system.