# Newton-Leibniz formula

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The formula expressing the value of a definite integral of a given function over an interval as the difference of the values at the end points of the interval of any primitive (cf. Integral calculus) of the function :

 (*)

It is named after I. Newton and G. Leibniz, who both knew the rule expressed by (*), although it was published later.

If is Lebesgue integrable over and is defined by

where is a constant, then is absolutely continuous, almost-everywhere on (everywhere if is continuous on ) and (*) is valid.

A generalization of the Newton–Leibniz formula is the Stokes formula for orientable manifolds with a boundary.