It goes without saying that integration is one of the fundamental concepts of single-variable calculus. However, there are in fact *three* concepts of integration that appear in the subject: the *indefinite integral* ∫ *f* (also known as the *antiderivctive),* the unsigned definite integral ∫_{[ab]} *f* (x) dx (which one would use to find the area under a curve, or the mass of a one-dimensional object of varying density), and the *signed definite integral* *f*(*x*) d*x* (which one would use, for instance, to compute the work required to move a particle from *a* to *b*). For simplicity we shall restrict our attention ...

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