There is an integrate option in the MapDataOntoElements that will integrate data over each volume element as it maps the data onto it.  It sounds like this is not what you need, though.  

I assume that you have a mesh for each structure that you are interested in.  In this case you could calculate a simple integral by performing the product of data of each element wight he volume of each element, then summing the resulting data.  In your case you can use the CalculateDistanceToField module to get a value for the distance to the point of rotation, then use ReportFieldGeometryMeasures to get the volume of each element, and CalculateFieldData to multiply these together ( there are other ways to do it too).  You would then use GetFieldData and ReportColumnMeasure to sum all the data together and the resulting 1x1 matrix would be your integral.  This method will give a good value if your elements are small enough.  If you are looking for something more complex than this or something like a finite volume solver, these aren't really implemented in SCIRun currently.  

Hopefully that helps.  

cheers,

Jess