Integral Function

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• Given a function ƒ of a real variable $x$ and an interval [a, b] of the real line, the definite integral $\int_a^b f(x)\,dx$ is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = $a$ and x = b. The term integral may also refer to the notion of antiderivative, a function $F$ whose derivative is the given function ƒ. In this case, it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.