Simple integration with limits

Hi All,
I have a linear projection(located along the y-axis) giving the heat loss/unit length for a simple rectangular channel located on the same axis. I simply want to integrate along this linear projection, and for any given y-location be able to tell what the heat loss is up to that point in the channel. I can't find a good description of how to do this. Some people suggest something about using a PDE, others seem to use the dest operator, but I can't get either to work. Adding an integration component coupling just gives me the total integral from 0 to y_max. Using integrate (expr,var,lower limit,upper limit) as follows integrate(....,y,0,y) gives me the correct values at the endpoints (y=0 and y=y_max), but in between is just a linear extrapolation it appears.

Any tips?
Thanks,
Bryan