I am doing a project on traffic flow, and am deriving the conservation equation between density and flux. I have got to this line in my calculations, and am unsure how to justify the step.
$$q(x_1,t)-q(x_2,t)=-\int_{x_1}^{x_2}\frac{\partial q(x,t)}{\partial x} dx $$
Does the FTC apply? I wasn't sure since we have a function of two variables in this case. In all of the sources I have used, they have taken this step as purely trivial, but I would like to know for certain why we are allowed to do this. Out of curiosity, is this always possible?
Many thanks in advance!