n. the definite integral of a real-valued bounded function, defined on a bounded interval as the value to which all Riemann sums,converge as their mesh-fineness tends to zero, where m(i) is the supremum (for the upper sums) or the infimum (for the lower sums) of the given function on the subinterval this exists if the function is continuous. Compare Lebesgue integral, improper integral.