Calculus Need help please thank you!

Question

Write the Riemann sum to find the area under the graph of the function f(x) = x² from x = 1 to x = 5. (4 points)

Answer Choices:

Answer 1

Here is a drawing of what you are trying to do:

The area of each rectangle between 1 and 5 is calculated as its width times its height. The width is 4/n which, in this case since n = 4 (because there are "4 points"), is 1. The height is for the left Riemann sum is just the function value or f(x) which is x²

So, the left Riemann sum will be (1)(1) + (4)(1) + (9)(1) + (16)(1). The summation equation that provides this is the third answer.

If you were doing the right Riemann sum you would get (4)(1) + (9)(1) + (16)(1).+ (25)(1) but that doesn't equate with any of the answers listed.