Question

Hello! This is my first question ever. I am in AP Calculus and am working on a redo. I know the correct answer but don't know how to arrive at the correct answer. Attached is the question and answer choices. Thank you for your help!

Answer 1

Since $\Delta x=\dfrac{b-a}n$, and you have a corresponding term in the given Riemann sum of $\dfrac5n$, you know the integral is being taken over an interval of length 5, so you can omit the second choice.

Next, $f(a+i\Delta x)$ corresponds to $a=3$ with $\Delta x=\dfrac5n$. The fact that $a=3$ alone tells you that the interval of integration starts at 3, and since we know the interval has length 5, that leaves the first choice as the correct answer.