real analysis - Is a periodic function differentiable? uniformly continuous?

Let $f : \mathbb R \rightarrow \mathbb R$ be a function such that $f(x + 1) = f(x)$ for all $x \in \mathbb R.$ Which of the
following statement(s) is/are true?

(A) $f$ is bounded.
(B) $f$ is bounded if it is continuous.

(C) $f$ is differentiable if it is continuous.
(D) $f$ is uniformly continuous if it is continuous.

It is a periodic function with period 1. I don't know how to proceed further...

Any Hints will be appreciated...