I'm currently trying to understand the proof of Itô's formula from the book of Revuz and Yor.
In the proof the integration by parts formula for continuous semimartingales is used. But to apply this I need to know that $f(X)$ is a continuous semimartingale if $X$ is a continuous semimartingale and $f$ is twice continuously differentiable.
Can you give any hint how this does hold? It would probably suffice if it holds for polynomial functions $f$.
Thanks in advance!