I was wondering if someone could show me the Riemann Sum for the following function:

$\displaystyle \sqrt{3}x^2 - x + 1 $ on [-1,2]

I need to find the exact area under the curve, so I'd assume n->INFINITY

I keep trying this, and I come in the realm of Mathematica's answer (If I split up the interval).. but not close enough.

I keep getting: -1 + 3i/n

Whenever I multiply everything out after substituting into the function, substituting in for i after factoring out the constant/n I come nowhere close.