Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential equations. This material should be of benefit to students because it reinforces one topic within another. Importantly, since the suggested approach is based on Taylor series, standard symbolic manipulation packages such as "Mathematica" can be used to simplify the resulting calculation. The article concludes with two specific examples for readers to try.