Consider teh partition $\displaystyle P_n$ of $\displaystyle [1,2]$, given by $\displaystyle P_n=\left \{ q_0,q_1,q_2,...,q_n \right \}$ where $\displaystyle q_n=2$. If $\displaystyle f(x)=x^j$ for some positive integer $\displaystyle j$, then evaluate the integral $\displaystyle \int_{1}^{2}f(x)dx$ by calculating the limit of the corresponding lower Riemann sums.

Can someone give me clues with this one.