The indefinite integral is the antiderivative, the inverse operation to the derivative.
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An indefinite integral may diverge in the sense that the limit defining it may not exist.
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Some authors define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.
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Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral.
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For instance, they are applied to the same physical processes, and they produce the same functions as outputs of the derivative and indefinite integral operators.
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When the word integral is used without additional specification, the reader is supposed to deduce from the context whether it is referred to a definite or indefinite integral.