variance of integral of Brownian motion

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If $W(t)$ is a Brownian Motion and $g(t)$ and $h(t)$ non-random functions defined as $X(t)=\int_{0}^{t}g(u)dW(u)$ and $Y(t)=\int_{0}^{t}h(u)X(u)du$.

Then we have $$Var[Y(t)]=\int_{0}^{t}g^{2}(u)(\int_{u}^{t}h(y)dy)^{2}du.$$

My question is: how to obtain the above equation?

Any motivation or insight is appreciated. Thanks.