Question About Radiative Transfer Equation Bounds of Integration

I’m unsure of what bounds to use for the integral involved in the formal solution to the radiative transfer equation. In some sources, the integral shown below goes from a general $s_0$ to $s_1$. In others, as below, the bounds start at 0 and end at a point $s$. Because there is an exponential term in the integral that depends on the path, the integral may give very different answers depending on the definition. In my case, I’m looking at two adjacent rectangular layers. The first layer goes from $x = 0$ to $x=x_0$ and the second from $x=x_0$ to $x=x_1$. The rectangular layers have different absorption coefficients. For the intensity calculation at $x=x1$ (in the case that radiation is coming from the first and second layers), I’m not sure if I should add the $I_{nu}(s_0)e^{-tau_{nu}(s_0, s)}$ term from layer 1 to an integral from $x_o$ to $x_1$ or if it makes more sense to compute the second integral from $0$ to $x_1-x_0$ because it is a different material. Please let me know if I can clarify the question.
begin{equation}
I_{nu}(s) = I_{nu}(s_0)e^{-tau_{nu}(s_0, s)}+ int_{0}^{s} j_{nu}(s’)e^{-tau_{nu}(s’, s)} ds’
end{equation}