# Thread: Fundamental Theorem of Calculus Part 2

1. ## 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

If f is continuous on [a, b], then the function g defined by

$g(x) = \int_a^xf(t)dt$ $a\le x\le b$
is continuous on [a, b] and differentiable on (a, b), and $g'(x) = f(x)$.
However, the FTC2 says that $\int_a^bf(x)dx=F(b) - F(a)$, 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?

2. Originally Posted by Chokfull
Can anyone help me understand this?
The FTC1 says, basically, that an integral of a function equals the antiderivative of that function, or
However, the FTC2 says that $\int_a^bf(x)dx=F(b) - F(a)$, 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?
What exactly does that question mean?

3. Never mind i realized I was being stupid :P