Approximations and Accuracy

I was hoping someone could help me or direct me to some reference for exploring the relationship between Midpoint and Simpson's approximations and accuracy of methods: En = Cn^p.

For example, I have calculated 3 approximations with decreasing *n* using each strategy.

I = integral( f(x) dx) from 0 to 1

Mn is a midpoint approximation

En = | I - Mn |

Then using the relationship En = Cn^p I am to determine the value of the constants C and p.

I can't figure this out and I've been trying and searching for similar examples for hours.

Thanks.