Do I need a DAC to go from computer to integrated

Do I need to have a DAC between the computer output and my integrated amplifier, if I want to improve sound?
Yeah you pretty much do. You need something to convert the digital to analog. You can either:

1. get a USB DAC, which are spouting up everywhere,
2. get some kind of computer soundcard (internal or external), or,
3. a USB to S/PDIF converter that can then be connected to any DAC that has
S/PDIF input (which most do).
A good internal soundcard is better than a crappy DAC.

That being said, I am using a USB DAC myself.
Yes, and preferably a USB DAC to skip the computer soundcard