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\begin{align*} \int_0^T W(t)\, dt &{}= \int_0^T\!\!\int_0^t dW(u)\,dt \\ &{}= \int_0^T\!\!\int_u^T dt\, dW(u) \\&{}= \int_0^T (T - u)\,dW(u) \\&{}= TW(T) - \int_0^T u\, dW(u) \end{align*} however i am not sure if it is what you are asking for


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I recenlty wokred on a similar problem and solved it with the help of Quantlib library. Assuming you are working with EUR and USD: get cross currency (xccy) swap data EUR / USD. You want to know how the xccy is collateralized and if Mark-to-Market resets apply to the USD leg. get interest rates swaps fixed vs ois / 3m / 6m in EUR and USD build USD/...



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