or lower Darboux sum, n. the weighted sum of the products of the infimal values of a function on a succession of subintervals of a given interval with the lengths of the subinterval; whence, the area, shown shaded below, between the x-axis and the step function of which the value in each subinterval is the infimum of the given function on that subinterval. The limit of this sum as the lengths of the subintervals tend to zero is the lower integral of the function. Compare upper sum. See Riemann integral.