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I'm having a bit of a hard time wrapping my mind around this concept. The part that seems to be troubling me the most is where Riemann Sums and sigma notation come in. I can't seem to find explanations online that help me better understand, so hopefully someone here could help?

The textbook that I am using is Briggs and Cochran's Calculus, section 5.1 specifically. For anybody that has this book, I have tried to follow example #5 as it seemed like it would be the most helpful. I have no clue what exactly they've done. The problem asks you to evaluate the left, right, and midpoint Riemann sums of f(x)= x^3 + 1 between a=0 and b=2 using n=50 subintervals. I can't figure out what to do once I have my Δx. The book just leaves me lost.

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# Approximating Areas Under Curves

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