Fundamental Theorem of Calculus Statement

Question

Which of the following correctly states the Fundamental Theorem of Calculus for a function $$f(x)$$ with an antiderivative $$F(x)$$?

Accepted Answer

If $$F'(x)=f(x)$$, then $$\int_{a}^{b} f(x)\,dx = F(b) - F(a)$$.

Answer

If $$F(x)=f'(x)$$, then $$\int_{a}^{b} f(x)\,dx = F(b) + F(a)$$.

Answer

If $$F'(a)=f(a)$$, then $$\int_{a}^{b} f(x)\,dx = f(b)-f(a)$$.

Answer

If $$F(x)=f(x)$$, then $$\int_{a}^{b} f(x)\,dx = F(a) - F(b)$$.

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