consider hull white model $dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$ when we solve the SDE above we have $r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha t}\int_{0}^{t}e^{\alpha u}dW(u) $ and when we take expectation and variance we have $r(t) \sim N(e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t}),\frac{\sigma^2}{2\alpha}(1-e^{-\alpha t}))$.
I know the calculate how find SDE and find expectation or variance but i don't understand why $r(t)$ has normal distribution.
thanks.