Laplace transform for RC integrator

This is my RC integrator:

From my two different analysises:

$$V_{out}(s) = V_{in}\dfrac1{sRC}$$

and

$$V_{out}(t) = \dfrac1{RC}\int V_{in} dt$$

These are of course different as one is in the frequency domain and one in the time domain.

If I understand correctly, $\mathcal{L}\{V_{out}(t)\} = V_{out}(s)$

However, Wolfram Alpha tells me $\mathcal{L}\{V_{out}(t)\} = V_{in}\dfrac1{s^2RC} \neq V_{out}(s)$

What am I doing wrong?