I was in Prof. Albert Milani’s Calculus class. He was telling us to calculate Riemann sums by hand. I was getting angry with him because there are much easier ways to find the area under a curve. So I decided to not bother calculating the Riemann sums by hand but simply use my nice shiny TI-89’s definite integral feature instead. Until I took the exam and was asked to show the difference in the limits arrived at by calculating the left, right, and center Riemann sums for an interval. I had, at that point, become so reliant on a solid-state computer that I had forgotten how to calculate Riemann sums. And I was very angry and yelled at the professor.
I have no idea why I forgot how to calculate a Riemann sum. If you can calculate the area of a rectangle, then you can calculate a Riemann sum. It’s even easier to find a left, right, or center Riemann sum since those have a constant period. But I guess the moral of the story is not to rely on solid-state equipment to solve your problems – you may need to get by without it someday.