I'm reading fundamental theorem of calculus in a wikipedia article and I didn't understand the meaning of the corollary:
If $F(x)$ is defined to be $F(x)=\int_a^x f(t)\ dt$ why do we need the theorem of calculus to prove this? using the definition of the $F(x)$ we see that $F(b)=\int_a^b f(t)\ dt$ and $F(a)=\int_a^a f(t)\ dt=0$.
What am I missing?
