Always remind myself that the (Reimann) integral is generally a sum: sum of the areas of all the rectangles under the curve. It becomes more accurate as their bases shrink (as x becomes smaller, and the rectangles become thinner. They eventually become almost lines, completely saturating area under the curve.)

The limit of their diminishing IS the Reimann integral. So it makes sense to use 'S' for sum.

Big-Sigma (∑) is used for summation in general, and Big-pie (∏) for products.