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)