Originally Posted by

**Plato** The real question here is “how does one partition the interval”?

If n=4 & the interval is [0,2] then **a** partition is: [0,.5],[.5,1],[1,1.5],[1.5,2].

That is known as a regular partition: each cell has length $\displaystyle \frac{{2 - 0}}{4}$.

The fact is we can take any partition. But I think your instructor mean the regular one.

Again, a Riemann sum can be formed using **any** set of points each selected from a different cell in the partition.

So if I were you, I would use a regular partition and use whichever type sum you want, but be sure to explain which you are using.