Can anyone help me understand this?

The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or

Iffis continuous on [a, b], then the functiongdefined by

is continuous on [a, b] and differentiable on (a, b), and .However, the FTC2 says that , where F is the antiderivative of f.

But why would it be the difference between two antiderivatives rather than just being an antiderivative in itself?