When I set up Cobertura inside Jenkins, I get URLs of the form:

http://jenkins.example.com/job/my-project/20/cobertura/subdiretory-in-code/

However, if my subdirectory is called 'api', e.g.:

http://jenkins.example.com/job/my-project/20/cobertura/api/

I get the 'Many objects of Jenkins provide the remote access API. They are available at /.../api/ where "..." portion is the object for which you'd like to access.' page instead. This is the same page as:

http://jenkins.example.com/api/

Looks like a bug in the URL configuration.