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An indefinite integral is the integral whose lower boundary is constant and whose upper boundary is variable and it should be distinguished from a primitive integral that just restores primitive functions. Constants of primitive integration should also be distinguished from constants of indefinite integration that the lower boundary produces. Integration is often said to be the inverse operation of differentiation, but it is mathematically false. Since a set of primitive functions and a set of integrands is not in one-to-one but in many-to-one relationship, integration cannot be an inverse mapping. Differentiation and integration are in the relationship of analysis and synthesis. As a derivative has only partial information on the original function, it cannot restore the whole information. Contents 1. The previous explanation of the indefinite integral 2. The indefinite integral should be distinguished from the primitive 3. Integration produces two kinds of constants 4. Integration is ...