Question

What is the fundamental theory of calculus?

Answer 1

The first fundamental theorem of calculus states that, if f is continuous function on the closed interval from [a,b] and F is the indefinite integral of f from [a,b], then:

\[\int\limits_{a}^{b}f(x)dx=F(b)-F(a)\]

Answer 2

Is that what you want? or did you want the second theorem as well?