Definite IntegralAn integral for which the limits of integration are specified is called a definite integral. The value of this integral is completely specified by performing the integration and substituting the values of the limits. This is in contrast to an indefinite integral which has no specified limits.

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Indefinite Integral An indefinite integral or antiderivative has no specified limits for the integration. For application to specific problems, boundary conditions must be applied to the result in order to arrive at a specific value for the integral. The uncertainty in the value of the indefinite integral is expressed in the form of a constant of integration which is not defined by the integration process. The constant of integration is determined by applying the relevant boundary conditions to the problem.

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Constant of IntegrationThe use of a constant of integration is a way to give a general result for an indefinite integral which arises in a physical problem. The process of integration does not give a specific value for the integral, but the application of physical boundary conditions makes possible the assigning of a definite value to the constant of integration, thereby fitting the calculation to the specific physical situation. 
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