Fundamental Theorem of Calculus Part 2

Can anyone help me understand this?

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

Quote:

If

*f* is continuous on [

*a, b*], then the function

*g* defined by

$\displaystyle g(x) = \int_a^xf(t)dt$ $\displaystyle a\le x\le b$

is continuous on [*a, b*] and differentiable on (*a, b*), and $\displaystyle g'(x) = f(x)$.

However, the FTC2 says that $\displaystyle \int_a^bf(x)dx=F(b) - F(a)$, 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?