The second part of the fundamental theorem of calculus is my favorite. Let f be a continuous real-valued function defined on a closed interval [a,b]. Let F be an antiderivative of f, that is one of the indefinitely many functions such that, for all x in [a,b], f(x)=F'(x) then $ \int_a^b f(x) dx $=F(b)-F(a)
