minimizing constraint problem

Question

Which curve joining the points (0,0) and (1,0) minimizes the integral $$ J[y]=\int_0^1(y'')^2 dx. $$ subject to the condition $$ \int_0^{1} (y')^2dx=1, $$ if $y(0)=0$, $y'(0)=\alpha$ and $y(1)=0$.