Answer
Fill the blanks with:
derivative; indefinite integral,
indefinite integral; derivative.
Work Step by Step
If $F(x)$ is an antiderivative of $f(x)$, that is
$\quad F'(x)=f(x)$,
then the indefinite integral of f is
$\displaystyle \int f(x)dx=F(x)+C.$
This is not one function -- it is a collection of functions, separated by some constant. These functions have the form:
$\quad G(x)=F(x)+C.$
So, taking a derivative of $F(x)+C$ (the indefinite integral), we obtain $f.$
First two blanks: derivative; indefinite integral.
But, taking the integral of $f(x)$ (the derivative of $F$),
we obtain $F(x)+C.$
Last two blanks: indefinite integral; derivative.
