Represent the limiting case of the Riemann sum as a definite integral. The definite integral of a continuous function f over the interval [a, b], denoted by ∫f(x)dx over limits a to b, is the limit of Riemann sums as the widths of the subintervals approach 0. A definite integral can be translated into the limit of a related Riemann sum, and the limit of a Riemann sum can be written as a definite integral.