posible bug - clashing variable names in integrals

You might want to reformulate integration, e.g.  make dint(f,a,b) the 
standard, where
f looks like lambda([x],x^2+sin(x) ....)

that is, an explicit function.

Then you can use rules comparable to alpha-  and beta- conversion in the 
lambda calculus in
proofs, if necessary.

This might simplify your bound/unbound stuff.   The integration syntax 
and the semantics associated
with variables suffer by having been written carelessly. The authors of 
the programs were more
concerned with the underlying algorithms than with the programming 
language or user interface
to access the algorithms.
RJF