Depends on what you mean by "integrate". If you want the build process to also build the Doxygen files you can add a "post-build" step to run Doxygen. Go to the project properties dialog, then "C/C++ Build", then "Settings". In the "Configurations" line up top select "all configurations", or perhaps only "release" if that is the only time you want to (re)create the doxygen files. Then under the "post-build steps" add the Doxygen command line.
If you want to edit the oxygen config file in the IDE, there are (or were) plug-ins for that. But CubeIDE's support for non-ST provided plug-ins is hit or miss.
