lithium battery with built in charger help

i want to add a lithium battery pack to my arduino but i want to be able to use the board while i charge the battery like with a cellphone but im not sure how to go about this. and i dont wanna buy anything already made cuz wheres the fun in that.

can anyone point me in the right direction?

ive got a few phones and smartphones that i can salvage parts off if its possible also

thanks in advance

Check maxim-ic.com for charger controller chips. I requested some samples of MAX1811 to use with a 1000mAH 3.7V Li Ion battery, waiting for them to arrive so I can try it. Minimal external parts needed.
Many other options available too if that one won't support simultaneous use.

let me kno if they work

microchip also make li-ion charger ICs that work well.