I wanna solve the following PDE of wave equation using Mathematica.

$ u_{tt}=u_{xx}$

$ 0<x<\pi , t>0$

Initial Conditions:

$ \begin{cases}u(x,0)=sin(x) \u_{t}(x,0)=1\end{cases}$

Boundary Conditions:

$ \begin{cases}u(0,t)+u_{x}(0,t)=1\u(\pi,t)+u_{x}(\pi,t)=-1\end{cases}$

- I know the boundary and initial conditions are inconsistent.

Are the following codes correct?

`weqn = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}]; ic = {u[x, 0] == Sin[x],Derivative[0, 1][u][x, 0] == 1 }; bc = {u[0, t] + Derivative[1, 0][u][0, t] == 1, u[Pi, t] + Derivative[1, 0][u][Pi, t] == -1}; sol = NDSolve[{weqn, ic, bc}, u, {x, 0, Pi}, {t, 0, 10}]; `