How do I set a shortcut to screenshot a selected area?

1. Open System Settings -> Keyboard -> Shortcuts
2. Select Custom Shortcuts(you can go to Screenshot-s too and it will work)
3. Click +
4. Fill fields
   • Name to Take a screenshot of area
   • Command to gnome-screenshot -a or shutter -s(if u prefer shutter)
5. Click OK
6. Double-click on what you make and set shortcut Shift+PrtSc

— And that's all ... ;)

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That shortcut is already built-in: Shift+PrtScr :)

The full-list of screenshot keyboard shortcuts is:

While to above answers worked for me in Ubuntu; after switching to Lubuntu I noticed that the ShiftPrtScn was no longer working.

The following procedure fixed it for me. Since in Lubuntu the program scrot is used, I found that I had to add the following to the ~/.config/openbox/lubuntu-rc.xml:

<!-- Launch scrot with interactive select when Shift-Print is pressed -->
<keybind key="S-Print">
  <action name="Execute">
    <command>scrot -s</command>
  </action>
</keybind>

After the change do not forget to issue: openbox --reconfigure to activate the updates.

See the Lubuntu documentation for more details.