How to deal with negative value in a Riemann sum question?
I'm doing a question where I need to prove that a function, $x^2 + 2x$ is Riemann integrable on the interval $[-3,3]$.
The question also gives me the interval $2n$, first $n$ intervals in $[-3,-1]$ with the width of $2/n$ and second $n$ intervals in $[-1,3]$ with the width of $4/n$.
I did two different summations and got to $(24n^2-9n+3)/(3n^2)$ for my lower Riemann and $(24n^2+9n+3)/(3n^2)$
When I limit both to infinity they are equal but they are not equal to the true area of $18$. Is my error due to not accounting for the negative area and if so how do I address it in my Riemman sum?
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