Let $f\in C^2$ and $(X_t)_{0\leq t}$ be a semimartingale.
We know from Ito's Formula $$ f(X_t) = f(X_0) + \int_0^t f'(X_{s-}) dX_s + \int_0^t f''(X_{s-}) d[X^c,X^c]_s + \sum_{s\leq t } ( \Delta f(X_s) - f'(X_{s-} ) \Delta X_s) $$
Now, this is a bit an awkward question, I guess I don't completely understand how to interpret the very last term.
I'm wondering what $\Delta f(X_t)$ is? I know that
$$
\Delta \int_0^t f'(X_{s-}) dX_s = \ f'(X_{s-}) \Delta X_s
$$
but what will the contribution from the last sum be? I guess what I can't seem to figure out is exactly what
$$\sum_{s\leq {t-} } ( \Delta f(X_s) - f'(X_{s-} ) \Delta X_s)$$ should mean.