In this paper, we study the numerical integration of continuous functions on d-dimensional spheres S d R d + 1 by equally weighted quadrature rules based at N>=2 points on S d which minimize a generalized energy functional. Examples of such points are configurations, which minimize energies for the Riesz kernel ||x-y|| - s , 0<s=<d and logarithmic kernel -log||x-y||, s=0. We deduce that point configurations which are extremal for the Riesz energy are asymptotically equidistributed on S d for 0=<s=<d as N->~ and we present explicit rates of convergence for the special case s=d, which had been open.