I have to find the solution to this problem:

$\displaystyle u_{xx}=u_{tt}+f(x,t)$

$\displaystyle u(x,0)=0$

$\displaystyle u_t(x,0)=0$

where f(x,t) is a step function:

$\displaystyle 1 $ for $\displaystyle |x|<= 1 $ and $\displaystyle 0< t < 1$

$\displaystyle 0 $ else

I know I have to use the duhamel's principle, but I have problem with the integration of f(x,t).

Can anybody help me please?

thank you