Why do we use capital F for the antiderivative of f, instead of simply f?
Consider the general equation df/dt=g 
Note I assume f and g are scalar functions of t.
To find the function f whose derivative is g, we simply take the antiderivative of g. So (using int(X) for indefinite integral of X) we can integrate both sides of :
Note the integral of df/dt is simply f(t) (with a constant added). So why is it conventional to use capital letter F for int(g), instead of just calling it f? That is, why add a '=F' to the end of ?
Why is this universal in the textbooks? What am I missing, as right now it looks like an unnecessary terminological layer, that even seems to hide the elegance of the relationship between the derivative and antiderivative?
Given its universality, I am assuming I am missing something. Please help!