A quadrature rule using Appell polynomials and generalizing both the Euler-Maclaurin quadrature formula and a similar quadrature rule, obtained by G. Bretti and P. E. Ricci [Georgian Math. J. 8, No. 3, 447–453 (2001; Zbl 0992.33004)], which makes use of Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the extrema of the considered interval, is derived. An expression of the remainder term and a numerical example are also enclosed.