Here I have this question
(i) state Ito's formula
(ii) hence or otherwise show that
$\int^t_0B_s dB_s = \dfrac{1}{2}B^2_t -\dfrac{1}{2} t$
(iii) define the quadratic variation $Q(t)$ of Brownian motion over [0,t], given that $Q(t) = t$, use this result to prove (ii)
I can do everything up to the last bit of (iii), how can quadratic variation tell you this relationship?
disclaimer: this is not homework. I am trying to help a friend preparing for an exam and this was a past paper question.