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I'm asked to find the quadratic variation of the integral $\int_{0}^{t} W_s^2 ds$.

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The quadratic variation of $$X_t=\int_0^t W_s^2\,ds$$ is 0. This is because it's an Ito process with no $dB_s$ term.

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    $\begingroup$ How do I prove it? Do I have to show the total variation is bounded, and then the quadratic variation is 0. $\endgroup$ – Geoff Chen Oct 9 '18 at 1:57

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