A new method for the approximation of integrals using the generalized Bernstein quadrature formula

In the present paper, we establish the theoretical framework of a new method in order to approximate a definite integral of a given function by the generalized Bernstein quadrature formula. Some numerical examples will be given as support of the theoretical aspects. We want to highlight an applicative side of the Bernstein polynomials, in contrast to the well-known theory of the uniform approximation of the functions.