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.
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.