No , you have to record it with something else ---> windows movie maker is good for recording web cam.
And here comes the tricky part. You have to put them together in a video editing ( any software which is supporting multiple layers )

can you record straight from internet explorer with Fraps.. I know how to use it for most games i.e. my youtube channel but I was wondering if it was possible to use it for sites like Kongregate or gamejolt (where you play the game from the browser instead of installing it. Let me know if you would. It would really help me out a lot. Thanks

For recording your browser and desktop and things like that, I recommend XSplit.
Agreed its a bit technical, but that's what I would look into. Its free, and if you want to subscribe its rather cheap, but the free version really isn't any different then the paid except a few more audio codecs.