# Comparison of variance of stochastic and non-stochastic integrals of the Brownian motion

Given that $$B_t$$ is the standard Brownian motion, I need to contrast the mean and variance of the stochastic integral $$\int\limits_{0}^t B_s dB_s = \frac{1}{2}(B_t^2 - t)$$ with the non-stochastic integral $$\int\limits_0^t B_s ds$$. So I obtain zero means for both of the integrals. I obtain $$Var(\int\limits_{0}^t B_s dB_s) = \frac{1}{2}t^2$$ while $$Var(\int\limits_{0}^t B_s ds) = \frac{1}{3}t^3$$. I am wondering what is the implication of this result? How should I interpret the observation that the stochastic integral of the Brownian motion has lower variance compared with the non-stochastic integral?