"$f\left(x\right)=-\frac{x^2}{3}-2$
We are supposed to calculate $\int _0^2\:\left(-\frac{x^2}{3}-2\right)dx$ using the limit definition of an integral.
a) Calculate $Rn$ for $f(x)$, which is the Riemann sum where the sample points are chosen to be right-hand endpoints of each sub-interval on the interval [0,2]. Write your answer as a function of n without summation signs.
b) Calculate the limit of Rn as n approaches infinity."
I think the main confusion I am having is with part a. How exactly am I supposed to find the Riemann sum without knowing the length of each sub-interval? Am I supposed to make each sub-interval $1/n$ and then keep going until $2n/n$. As these would be the right endpoints? If so, how would I calculate the sum of these seemingly infinite amount of intervals? Or am I supposed to approach this problem in a different way?
Any help?