Recall the definition of teh Riemann Sum S(f;\pi ;\xi) for a function f:[0,1]\rightarrow \mathbb{R}.
Let f:[0,1]\rightarrow \mathbb{R},\ x\rightarrow \frac{5}{6}x[/latex] For the partition \pi_n of [0,1], 0=t_0<t_1<...<t_n,\ t_j\ =\ \frac{5}{n},\ j=0,...,n and \xi_j =\ \frac{2}{3}t_j\ +\ \frac{1}{3}t_(j+1)\in [t_j,t_(j+1)] find S(f;\pi_n,\xi).

Now Prove lim(n\rightarrow infinity)\ of\ S(f;\pi_n,\xi)=\frac{5}{12}

Pretty clueless on this question. A walk through on the steps would be nice for the test coming.