Banshee 2.1.3 is the second release in the 2.1 development series leading up to 2.2 (versions 2.1.1 and 2.1.2 were not released). You can upgrade Banshee using the banshee daily builds ppa.
To upgrade Banshee open a termninal window (press Ctrl+Alt+T) and copy+paste the following two lines:
sudo add-apt-repository ppa:banshee-team/banshee-daily
sudo apt-get update
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