My issue is that when im driving my car with the a/c off its fine nothings happening. As soon as i turn on the a/c though i hear squealing for a couple of secs/mins and goes away after throttle or just driving. The belt seems fine and seems to have tension(will double check) but this i guess hat on my pulley that when giving it throttle or high RPM it pulls out from the pulley and then comes back in; upon coming back in it squeaks. Why does it do this and why is it causing my teg to squeak?

Doesnt seem relivant but its a 99 DC2

 

If "squeal" is only there when A/C is on, [A/C compressor cycling on] then it is most likely the compressors front shaft bearing on it's way west, time to replace the compressor.
Your 99 Integra uses a Nippondenso 10PA15C, can be found at your local Cooling Depot, [Four Seasons] distributor, [auto parts store] for about half the price of the Acura part, also available as a remand, Four Seasons part # is 97335, you will also need the filter/dryer part #33588, or you can make a trip to your local PicknPull, the compressor is found in 98-01 Integra, 99-00 Civic and 96-97 DelSol. 94

 

You say the belt has tension, but is it the proper tension. If not, the belt will slip. It sounds like you just need to tighten the belt a little bit more. I would try this before spending about $100 for a used compressor, $30 for a new dryer, and $60 to recharge the system.... It sounds like the belt is just slipping a bit when cold.

If the free fix doesn't work, then the bearing is shot.

 

Ditto the above^^^, make sure belt tension is correct, you should also check belt for glazing, [check inside of belt for shiny surface] indication of slipping belt. 94

 

yup i can say from experience i replaced my compressor due to that same issue. i thought it was the compressor clutch but it turned out to just be the belt tension. good thing i do hvac for a living so i was only out the cost of the compressor. the belt seemed to be tight to me but i guess it wasnt. i just tightened it almost until i couldnt anymore.