I know this is certainty a basic question, but I'm wondering what you could use as an alternate name for the integral of a function. That is to say; $$\text{In } \int f(x)dx=F(x) \text{, } f(x) \text{ is the integrand} $$$$\text{What would you call } F(x)? $$
I apologise for asking such a basic question, but I was unable to find any information about this online (although I suspect that's most likely due to my own inability to adequately word my queries)
Any help is greatly appreciated.
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$\begingroup$Antiderivatives can be used to compute definite integrals, using the fundamental theorem of calculus: if $F$ is an antiderivative of the integrable function $f$ over the interval $[a,b]$, then:
$$\int_a^bf(x)dx=F(b)-F(a)\tag1$$
Because of this, each of the infinitely many antiderivatives of a given function $f$ is sometimes called the "general integral" or "indefinite integral" of $f$ and is written using the integral symbol with no bounds:
$$\int f(x)dx\tag2$$
If $F$ is an antiderivative of $f$, and the function $f$ is defined on some interval, then every other antiderivative $G$ of $f$ differs from F by a constant: there exists a number $c$ such that $G(x)=F(x)+c$ for all $x$. $c$ is called the constant of integration.
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