What must be true of f(x) and g(x) if both are antiderivatives of f(x)?

For a function f(x) to be anti-derivative of F(x), f'(x) should be equal to F(x).
Similarly, for g(x) to be anti-derivative of F(x), then g'(x) should be equal to F(x).

From this we can deduce that for both f(x) and g(x) to be anti-derivatives of F(x), then f'(x) should be equal to g'(x)