In effect, (1.2) provides an interpolation formula for gn (x) in terms of the gn (tnk ) . There have been many studies of this approximation method, mostly with g (x), h (x) and K (x, y) continuous for 0 < x, y < 1. Recent references include Buickner [1], [2], [3], Kantorovitch and Krylov [4], Mysovskih [5], [6], [7], Brakhage [8], Anselone and Moore [9], and Anselone [10]. For further references, see [2], [3], [4], [10]. In this paper we deal with a certain class of integral equations with possibly discontinuous kernels. Only real equations are treated, sinlce the methods of analysis depend heavily on the order structure of the real line. Extensions to complex integral equations will be made elsewhere. As for the quadrature formula, assume