Problem: Use Riemann Sums to approximate the area under the curve

f(x) = 5x^2 + 1 on [0,2] using left endpoints and n=4

The attached image is my professor's work (this is a study guide for my exam). After finding change in x (y-x)/n or 2-0/4 = 1/2 in this case...I'm pretty much lost. Specifically...where is the prof getting the 3/4 from in f(3/4) on the right side of her work? Does the 1/2 come from the change in x or is that just coincidental?

Thank you very much!

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Okay, I see what is going on with 1/2 and 3/2. the Area = (change in x)(sum of each segment).

However, why do I only add f(0) + f(1/2) + f(1) + f(3/2)? Why do I not add f(2), where the last subinterval ends?

Thanks!

Aye, I've figured it out myself. "Using left endpoints" = use the lines to the left of the subintervals, so f(2) would not be included.

Thanks to anyone who may have read this

Admins: Is there any way to signify that a question is resolved or to delete it? Thanks!