We envisage here that it is desired to evaluate (using a digital computer) the integral of a function f (x, y) with respect to x (say), along a curve γ in the xy-plane; the value of the function and of the co-ordinates of the curve being known only at discrete, and possibly irregularly spaced, points of γ. Such a problem frequently arises, especially where γ is a closed curve: as for instance in aerodynamics when it is desired to estimate the force components and pitching moment inferred from an experimentally determined set of pressures taken over an aerofoil; here the function values are related to the pressure measurements and γ is the aerofoil contour.