Use pack of 8xC size Ni-MH wired for 5.6v as power supply for Raspberry Pi
There is already an onboard linear voltage regulator on the Raspberry Pi(1) that takes you from X to 3.3V

However, the Vdd on the USB-port is connected straight to whatever you're powering your Raspberry Pi with. That is so you can power things at 5V, such as a keyboard or a mouse if you power the Raspberry Pi with a regular 5VDC adapter from the outlet. 

So you can hook up those batteries straight away into the Raspberry Pi's power jacket, but do not expect to be able to use the USB, since as Passerby wrote in your comment, you get 4.8V, and not everything is 4.8V tolerant, and as time goes by those batteries will go lower to say 4 volt and I'm not sure how many keyboards or mice or USB sticks that are made for those voltages.


The linear voltage regulator is in RG2 in the image above. 

For other raspberry pi's (that is not RPI1), check out the Raspberry Pi stackexchange