Antiderivative

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral^{[Note 1]} of a continuous function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f.^[1][2] The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as F and G.

Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function is Riemann integrable is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

In physics, antiderivatives arise in the context of rectilinear motion (e.g., in explaining the relationship between position, velocity and acceleration).^[3] The discrete equivalent of the notion of antiderivative is antidifference.

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