For numerical integration, Simpson's Rule is:

$\displaystyle \int_{x_0}^{x_2} f(x) dx = \frac{h}{3} (y_0 + 4y_1 +y2) - \frac{h^5}{90} f^{iv} (c)$

where $\displaystyle h = x_2 - x_1 = x_1 - x_0$ and $\displaystyle c$ is between $\displaystyle x_0 $and $\displaystyle x_2$.

There is however a conventional error which arises when using Simpson's rule to approximate an integral.

An expression for this error can be derived using Taylor series, but I'm having trouble deriving it. Can anyone please help?