Actually updated Maple 16 is able to do the shown integral correctly:
| sin(a x)
| -------- dx
> diff(%, a);
| cos(a x) dx
Replacing b by infinity gives the matching expressions (the particular result is undetermined for b=infinity but this is just an example).
Actually the problem is general, another simpler example gives the same error message:
Error, (in diff/Int) invalid Int(...) format
The bug results from diff trying to differentiate the option part from the integral. If method= is removed, one gets a wrong double integral
| | x dx d_d01amc
This time the integrand is differentiated correctly but the option _d01amc is taken as a variable and the result is a double integral!
I need to use method=_d01amc in a more complicated integral before differentiating because the result then needs to be evaluated numerically fast enough in plots, which is only possible by using a method of integration using the NAG library.