Wave equation $u_{tt}=u_{xx}$ with range $-\frac{x}{2}<t$ and "initial conditions" at $u(x,-\frac{x}{2})$ and $u_x(x,-\frac{x}{2})$

Question

Wave equation $u_{tt}=u_{xx}$ with range $-\frac{x}{2}<t$ and $-\infty<x<\infty$. "initial conditions": \begin{align} u\big(x,-\frac{x}{2}\big) &= \begin{cases} 1, & |x|<1, \\ 0, & \text{else}. \end{cases} \\ u_x\big(x,-\frac{x}{2}\big) &=0 \end{align}

find $$\int_{\frac{3}{2}}^\infty u(x,0)\, \mathrm{d}x$$

I struggle to understand how to use the range $-\frac{x}{2}<t$ and the fact the that the "initial condition" are at $t=-\frac{x}{2}$.