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Antiderivatives of Basic Functions. The fundamental use of integration is as a continuous version of summing.Integral Calculus Formula Sheet. Integration is the basic operation in integral calculus. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Type in any integral to get the solution, steps and graph. Integral will give the total distance at any given time. Use substitution, setting u=−x, and then du=−1dx. Integration, the first being that integration is in- verse to differentiation. As you become more familiar with integration, you will get a feel for when to use definite integrals and when to use indefinite integrals.