Please explain the antiderivativeCan someone please explain what an antiderivative is. Is there a rule...

Explanation:
An antiderivative of a function f, with domain D, is a function F, with domain D, such that $\frac{d}{dx}F(x)=f(x)$ for all $x\in D$. If F and G are antiderivatives for f, then $F(x)=G(x)+C$ for all $x\in D$ and for some constant C. One can find the family of antiderivatives (which contains all antiderivatives, where they only differ by a constant) by computing the indefinite integral of f:
$\int f(x)dx=F(x)+CC\text{ is a constant}$ provided f is integrable of course.