Fubini's theorem in Stochastic Integral

The short rate under the Merton model is

$r_t = r_s + \theta (t - s) + \sigma \int_s^t d w_u$

Now we integrate above to get bond price from s to T

$\int_s^T r_t \, dt = \int_s^T r_s \, dt + \theta \int_s^T (t - s) \, dt + \sigma \int_s^T \int_s^t d w_u \, dt$

This simplifies to below.

$=r_s (T - s) + \theta \int_s^T t \, dt - \theta s \int_s^T dt + \sigma \int_s^T \int_s^T d w_u \, dt$

Order of integration is changed for the last double integral. I am not able to understand the order change using Fubini's theorem. Though the order is changed the outer integral bound remains same.

Any explanation on this order change would be greatly appreciated!