Differential Eq. - Separation of Variables

Solve the following Differential Equation:

$\displaystyle \frac{dy}{dx}=x(1-y)$ , $\displaystyle y(1)=0$

$\displaystyle \frac{1}{1-y}dy=xdx$

$\displaystyle u= 1-y$ , $\displaystyle du=-1dy \rightarrow dy=-du$

$\displaystyle -\int \frac{1}{u}du=\int xdx$

$\displaystyle -\ln(u) = \frac{x^2}{2} + C \rightarrow -\ln(1-y)=\frac{x^2}{2} + C$

$\displaystyle \ln(1-y)=-\frac{x^2}{2} - C \rightarrow 1-y=e^{-\frac{x^2}{2} - C}$

$\displaystyle y=-e^{-\frac{x^2}{2} - C} + 1$

Did I do up to here correctly?