Find the limit of a Riemann Sum The function is $f(x) = 1-x^2$. I'm stuck as I can't factor the expression in the last line to find the limit.


The expression from your last line can be simplified:
\begin{align} 
\frac{1}{n} \bigg[n-\frac{1}{n^2}\bigg(\frac{n(n+2)(2n+1)}{6}\bigg)\bigg] 
&  = \bigg[\frac{n}{n}-\frac{n(n+2)(2n+1)}{6n^3}\bigg] \\[0.1in]
& = 1-\frac{1}{6} \bigg( \frac{n+2}{n} \bigg)\bigg(\frac{2n+1}{n}\bigg) \\[0.1in]
& = 1-\frac{1}{6} \bigg( 1+\frac{2}{n} \bigg)\bigg( 2+\frac{1}{n} \bigg)
\end{align}
