I got this interpretation:

If we have $y'(t)=u(t)$ , it's like have $y(t)=\int{u(t)dt} $

If we solve this simple equation, we obtain:

$$sY(s)=U(s)$$
$$Y(s)=\frac{U(s)}{s}$$

So, we have the $U(s)$ multiplied for $\frac{1}{s}$

Is this conjunction correct? It doesn't seem quite complete. What do you think?