Every continuous function has an antiderivative
I thought this statement was false, but it seems that it is true.
I thought that it suppose to be every antiderivative is a continuous but the other way around is wrong. Similarly, when you say every continuous functions is not a derivative, but every derivative is a continuous.
If $F(x) = \int_0^x f(t) \, dt$, then $F(5) - F(3) = \int_3^5 f(t) \, dt$
If $F(x) = \int_0^x f(t) \, dt$ and $G(x) = \int_2^x f(t) \, dt$ then $F(x) = G(x) + C$
False, it seems weird to me. I do not have a logical reason.
Could anyone check my answers and tell me if I am right or wrong?