The generalization of the integral formula with three nodes is introduced, and some sharp and the best possible inequalities for the functions whose higher order derivatives belong to L p spaces are given. We establish non-weighted version of the three point integral formula. From the general non-weighted formula we shall get the famous Simpson, dual Simpson and Maclaurin formulae. Some new errors of approximation in these integral formulae are obtained. © 2019 Element D.O.O.. All rights reserved.