Suppose
$u_t+\alpha u_x =\int\limits_{b-h}^{b} u(t,x) dx $
$u=u(x,t), (x,t)\in ([a,b]\times [0,T])$
with initial data $ u(x,0)=u_0(x)$, h is fixed xonstant. I want to solve this equation by using finite volume method (FVM). I can apply FVM for such type of conservation laws with source term like $ u_t+au_x=S(u,x,t)$. But if $S(u,x,t)=\int\limits_{b-h}^{b} u(t,x) dx $ I have no idea how to tackle the right-hand side of the above differential equation. Can you provide me some suggestion.