I need to find the Green’s Function for the problem

u'' = f(t); u(0) = 0; u(1) = 1

I know that the general solution of the homogenious equation is

u=at+b

where a and b are constants, and the Green's function is

G(t,z)=(u1(z)*u2(t)-u2(z)*u1(t))/W(z)

where u1 and u2 are independent particular solutions of the homogenious equation, but I'm not sure how to apply the initial values to find the right u1 and u2. Can someone please point me in the right direction?