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 $$x = -1$$.