The purpose of this paper is to clarify the evaluation of path dependent integrals in the energy function method for stability analysis in power systems. lit the literature these are handled in an approximate manner through straight line approximation leading to closed form analytic expressions of the energy functions. This may not always be accurate, Here it is compared with the trapezoidal method of integration along the faulted trajectory as originally proposed by Athay et al. The paper also emphasizes some tutorial aspects for explaining the PEES and the BCU method.