So to verify, you see something like this?
If so, FIRST try the repair utilities mentioned before.
If they fail, you can just click in the space I have marked [Former Mac OS X], choose a format (Mac OS Extended Journaled is best,) and click Apply. That will create a brand-new partition you can install OS X in. Your 10 GB partition is the Windows partition, and trying to install there would just break your Windows installation.
Note: If you can't recover the OS X partition, and the Windows partition is broken as well (and you don't have anything worth saving,) then you would be better off just reformatting and starting over. To do that, choose "1 Partition", make it Mac OS Extended Journaled, install OS X, then run Boot Camp to install Windows.
When installing Windows through Boot Camp
follow the directions about which partition to install on!