TITLE: Quadratic variation of $X_t=\int_0^t B_s \, ds$
QUESTION [6 upvotes]: Let $B$ be a standard brownian motion and
$$
X_t=\int_0^t B_s \, ds.
$$
What is the quadratic variation  $[X]_t$ of $X$?
I see $dX_t$ as an sde with drift term $B_t$.

REPLY [6 votes]: $[X]=0$ since $X$ has finite variation.