Picard's theorem on Second Order Differential Equation

Question

I am being asked about the following equation:

$-u'' + L * \sin(u) = f(x)$

with initial conditions

$u(0) = 1, u(1) = 0$

I feel puzzled as there is no initial condition for a derivative of $u$. Can I proceed without it? How do I manage both initial conditions of $u$?