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Discuss the role of constant of integration in indefinite integrals, why we don't involve it in definite integrals? (Be precise)

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Constant of integration is used to expresses the vagueness inherent in the construction of anti-derivatives. In the equation, C is used to refer to arbitrary constant known as the constant of integration. You can check out http://mathworld.wolfram.com/ConstantofIntegration.html for more information.

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