Originally Posted by

**Mollier**

$\displaystyle |E_2(f)| \leq \frac{M}{6}\int^h_{-h}|x(x+h)(x-h)|dx.$

The integral however, is zero and so I end up with a useless error bound. In one of my books they state a similar thing, but instead of using $\displaystyle -h,0,h$, they use $\displaystyle a,\frac{a+b}{2},b$ to get,

$\displaystyle |E_2(f)| \leq \frac{M}{6}\int^b_{a}|(x-a)(x-\frac{a+b}{2})(x-b)|dx.$

I've tried plugging the integral into wolframalpha and get zero here as well. The book though ends up with,

$\displaystyle |E_2(f)| \leq \frac{(b-a)^4}{196}M$.

Am I doing something wrong here? Are there easier ways of deriving Simpson's along with the error term?Any comments are highly appreciated! Thanks.