I am looking for practical error estimates for Newton-Cotes Quadrature rules.

Most books on numerical methods I have found mainly deal with theoretical error bounds/estimates for the respective methods.

Despite an extensive (but perhaps misdrirected) search I found almost nothing dealing with error estimation when automatic computation is concerned.

Example:The error of the Simpson-Rule is given by: $Ch^5 f^{(4)}(\xi) $ where $C$ is a constant and $\xi \in [a,b]$. Obviously $\xi$ usually is not known. One could certaily choose the maximum of $f^{(4)}$ to get an upper bound but this can be tricky to determine on the run.

This is why I am wondering: **what are the best practices for estimating Integration-Error in numerical algorithms ?** (above all I am interested in the ones concerning newton-cotes-quadrature)