You can upgrade it just fine. If you open a terminal, you can upgrade with one command: sudo do-release-upgrade and the Update Manager GUI will also give you the option to upgrade from LTS to LTS. You can even go into your sources.list file and change all referenes of one release to another release, eg: "precise" to "trusty", then do an apt-get update and then apt-get dist-upgrade, but this is not a recommended method to upgrade with.
In future (or if you plan to do it now), consider making a minimum of two partitions for your Linux install - one for the root filesystem "/" of 20GB or more and a dedicated one for the home filesystem "/home" of the remainder of your drive. You can skimp on having a swap partition if you have 4GB or more of RAM if you're an average user.
The reason you split it like this will allow you to do a complete fresh install of Ubuntu without stomping all over your home data because the installer can be told to mount Partition XYZ as "/home" but then you uncheck the box to format that partition. The installer will set it up and when you boot into it, it will happily re-use your existing /home data with the worst of your housekeeping being perhaps changing UID's and GID's if your new user account doesn't have the same UID/GID as the old account (a big recursive chown command will fix that).
And best of all is that through the entire process, your Windows 7 installation will be preserved. During the Ubuntu install, just delete the old Ubuntu partition(s) to recreate your new layout, but do not touch the Windows one(s). The installer will set Windows up in the GRUB menu whichever way you go.