Expansion Into Bernoulli Polynomials Based on Matching Definite Integrals of Derivatives

A method of function expansion is presented. It is based on matching the definite integrals of the derivatives of the function to be approximated by a series of (scaled) Bernoulli polynomials. The method is fully integral-based, easy to construct and presumably slightly outperforms Taylor series in the convergence rate. Text presents already known results.