Im having trouble setting up this Reimann Sum. The question is

Find the Riemann sum forf(x) = sin(x) over the interval [0, 2π],

wherex_{0}= 0,x_{1}=π/4,x_{2}=π/3,x_{3}=π, andx_{4}= 2π, and

wherec_{1}=π/6,c_{2}=π/3,c_{3}= 2π/3, andc_{4}= 3π/2. (Round your answer to three decimal places.)

So heres what i understand. n = 4, so there are 4 rectangles of uneven size. x_{0}- x_{4}are the given intervals.

I m guessing i should take $\displaystyle \sum_{i=1}^{n}$$\displaystyle f(c_i)\Delta{x_i}$ and set it up like this $\displaystyle \sum_{n=0}^{2\pi}sin(c_i)\Delta{x_i}$.

But thats where im stuck. Do i evaluate each right end point times $\displaystyle \Delta{x_i}$ and add them up? Does $\displaystyle \Delta{x_i}$ = $\displaystyle \frac{2\pi}{n}i$ or $\displaystyle \frac{2\pi}{4}i$

Any help is greatly appreciated.