Error estimates in local quadrature

A theoretical error estimate for quadrature formulas, which depends on four approximations of the integral, is derived. We derive a bound often sharper than the trivial one which requires milder conditions to be satisfied than a similar result previously presented by Laurie. A selection of numerical tests with one dimensional integrals is reported, to show how the error estimate works in practice. It turns out that, for reasonable values of the estimated relative error, we get both reliability and sharpness