ScreenRec
I switched to ScreenRec from previously using Free Cam.
ScreenRec gives you a little toolbar that hovers over all your desktop windows and allows you to start recording by dragging your viewing area with click and drag, and then counts down to start the recording. Through the settings you can choose where it records audio.
It has a 5-minute limit in the free version, a 1080 x 800 resolution limit in the free version, and saves to MP4 by default. So this is a great tool to graph a quick screen recording of an example. I don't remember the framerate being so great, but that may depend on your computer.