Answer
No.
We need a point on the graph of our function G(x) (we need to know one value $G(a)$).
Work Step by Step
If $F(x)$ is an antiderivative of $f(x)$, that is $ 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
$\quad G(x)=F(x)+C.$
More information is needed to pinpoint C, which would give a particular solution.
For example, if $G(x)$ is the actual function from the set of antiderivatives, and we know one point on the graph of $G,\quad (a, G(a))$, then we find C by inserting
$G(a)=F(a)+C$
