Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration. Calculate a definite integral using areas and properties of definite integrals. In some cases, a definite integral can be evaluated by using geometry and the connection between the definite integral and area. Properties of definite integrals include the integral of a constant times a function, the integral of the sum of two functions, reversal of limits of integration, and the integral of a function over adjacent intervals. The definition of the definite integral may be extended to functions with removable or jump discontinuities.