The fundamental theorem of calculus specifies the relationship between the two central operations of calculus, differentiation and integration. The first part of the theorem, sometimes called the first fundamental theorem of calculus, shows that an indefinite integration[1] can be reversed by a differentiation. The second part, sometimes called the second fundamental theorem of calculus, allows one to compute the definite integral of a function by using any one of its infinitely many antiderivatives. This part of the theorem has invaluable practical applications, because it markedly simplifies the computation of definite integrals. The first published statement and proof of a restricted version of the fundamental theorem was by James Gregory (1638-1675)[2]. Isaac Newton (1643-1727) and Gottfried Leibniz (1646-1716) independently developed the theorem in its final form.
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