If the Poisson integral is $$\int\int_S P(r,r')u_0(r')dr'$$ And gives the solution to the boundary value conditions $\Delta u(r)=0$ for |r|<1 and $u=u_0$ for |r|=1 The Poisson kernel being $$P(r,r')=\frac1{4\pi} \frac{1-|r|^2}{|r'-r|^3}$$
How would one go about proving that $$\int\int_S P(r,r')dr'=1$$ if |r|<1?