Since the function $f(x)$ is continuous in the closed interval $[a,b]$ and differentiable in the open interval $(a,b)$, so the function $F(x)$ will be continuous in the interval $[a,b]$ and satisfied all the conditions of Rolle's theorem.
In above text, they had used third braces [] when talking about continuous of a function. And, they used first braces () when talking about differentiability. Is there any deep meaning of different braces? All the things I know that is there's no differences, Is there?