Option + b results in ∫ Instead of Jumping Back a Word
Option-B has always been mapped to ∫ in OS X, and option-B has never been mapped to jumping back a word in emacs. What you're thinking of is the meta-B shortcut, which is only sometimes mapped to the option key depending on the app. In the Terminal you can enable it by going to Preferences > Settings > Keyboard and checking "Use option as meta key".

You're also probably confusing it with the Ctrl-B keyboard shortcut to jump back one character. That's the emacs shortcut that is available in all OS X apps. You can jump back one word using option-Ctrl-B, delete one word using option-Ctrl-D, etc.

If you want to use option-B and the other emacs shortcuts across all apps, you'll need to install some additional software for triggering the emacs behaviors when pressing the OS X keyboard combinations, as seen in this thread:

Emacsify OSX throughout: word-forward (⌥ + F) and word-backward (⌥ + B) instead of 'special characters'?