Are Anti-Derivatives Unique?

Suppose we have a function $f(x)$ that is differentiable, such that $f'(x)$ is continuous. Evaluate whether the following two statements are true or false.

(1) $f(x)$ is the only anti-derivative of $f'(x)$.

(2) The derivative of the integral function $\int_{2017}^x f'(t)\,dt$ (with respect to $x$) is necessarily $f(x)$.