Differentiability of a Piecewise Function

Let the function $h$ be defined as follows:

$\displaystyle h(x) = \begin{cases} \displaystyle x^2 + 2x + 2 & \text{if } x < -1 \\ \displaystyle -x + 3 & \text{if } x \geq -1 \end{cases}$

Which of the following statements about $h$ are true?

I. $\displaystyle \lim_{x \to -1^-} h(x) = \lim_{x \to -1^+} h(x)$

II. $\displaystyle \lim_{x \to -1^-} h'(x) = \lim_{x \to -1^+} h'(x)$

III. $h$ is differentiable at $x = -1$.