A new quadrature formula has been proposed which uses weight functions derived using a probabilistic approach, and a rather-ingenious 'Fusion' of two dual perspectives. Unlike the complicatedly structured quadrature formulae of Gauss, Hermite and others of similar type, the proposed quadrature formula only needs the values of integrand at user-defined equidistant points in the interval of integration. The weights are functions of the impugned variable in the integrand, and are not mere constants. The quadrature formula has been compared empirically with the simple classical method of numerical integration using the well-known "Bernstein Operator". The percentage absolute relative errors for the proposed quadrature formula and that with the "Bernstein Operator" have been computed for certain selected functions and with different number of node points in the interval of integration. It has been observed that the proposed quadrature formula produces significantly better results.
