Definition of class of continuously differentiable functions on a closed interval

This is a technical simple question. The space $C^1([a,b])$ is defined as

$$C^1([a,b])=\{f:[a,b]\to R: \exists\; f' \textrm{ and is continuous on } [a,b] \}.$$

I think there is some explaining to do here, and is the fact that $f'$ cannot be defined at $a$ or $b$ because those points do not belong to the interior of the domain. The question is:

In the above definition, $f'(a)$ and $f'(b)$ are understood in the sense of right and left derivatives respectively? If not, in which sense?