How to get Integrate to determine units

In a similar fashion to the question asked here, I am having trouble trying to get Integrate to correctly determine the units of the integrand:

Here I have plugged in specific values into the general formula that I am using and still Integrate can’t determine the units. The common theme between this post and the one given above is that we both need to integrate a piecewise function. What are we missing? Please note that my function is continuous at the joining of the two sides of the piecewise function.

EDIT: Here is the code in as nice a form as I could make it.

Integrate[
 Piecewise[
  {
   {
    ((Quantity[1, "Micrometers"] + Quantity[0.5, "Micrometers"])*
       Quantity[1, "Centimeters"*"Ohms"])/(y/
        Tan[Quantity[45, "AngularDegrees"]] + (Quantity[1, 
          "Micrometers"] - Quantity[0.5, "Micrometers"])),
    y/Tan[Quantity[45, "AngularDegrees"]] <= 
     Quantity[1, "Micrometers"] + Quantity[0.5, "Micrometers"]
    },
   {
    Quantity[1, "Centimeters"*"Ohms"],
    True
    }
   }
  ], 
   {y, Quantity[0, "Micrometers"], Quantity[10, "Micrometers"]}
 ]