Re: integration??
No
Integration means your users can log in to either bbPress or WordPress and be logged in in the other application. That’s all the built in integration accomplishes.
If you want the cross-posting between bbPress and WordPress, you want bbSync.
https://bbpress.org/plugins/topic/bbsync/
https://bbpress.org/forums/tags/bbsync
https://bbpress.org/forums/topic/bbsync-broken-plugin-like-it-bb-10#post-18577
Also, integration has nothing to do with the visual look and feel of bbPress. If you want to make bbPress look like your WordPress installation, you need to modify a theme to look like it (CSS and XHTML work.)
Pretty thorough discussion of what works and how to do it:
https://bbpress.org/forums/topic/wordpress-and-bbpress-integration-101
