Quadratic variation of $e^{B_t}$ where $B_t$ is the standard brownian motion.

Question

Consider $f(x) = e^x$ , then show that $<f(B)>_t$ is equal to $\int^t_0e^{2B_t}dt$.

1. I know from jensen's inequality that $e^{B_t}$ is a submartingale. How is quadratica variation defined for that? For a square integrable martingale $X_t$ it is the natural increasing process of the D-M decomposition of $X^2_t$
2. Do i somehow have to use ito's formula to get the answer? i tried, but could not get anything.