First, mathematics is not physics! And not every mathematical operation has a physical interpretation. Here, however, we can, after a fashion, give this a physical interpretation. If we have a solid, of volume, V, with "heat capacity" [itex]\mu[/itex], then, by definition of "heat capacity", the total heat in that object, at constant temperature T, is [itex]\mu TV[/itex]. If the temperature, and/or heat capacity, varies from point to point, say T= T(x,y,z) and [itex]\mu= \mu(x,y,z)[/itex], then we have to integrate to find the total heat: