It is possible to play games using integrated graphics as long as the games are not graphically intensive. I set up Skyrim Legendary Edition to run on a friend's laptop which has a Core i5-4210u and the Intel HD 4400. He was happy enough with the 30 FPS he was getting at 1600x900 resolution with medium graphic settings, but no shadows and no anti-aliasing. He could get 40+ FPS at 1366x768 resolution, but he preferred playing at the higher resolution.
As for Sims 3, I have personally seen it played on an older laptop at 1366x768 resolution with a core i3 / i5 and the Intel HD 3000 which is less powerful than the new Intel HD 4400 that is in Intel's 4th generation CPUs. Below is a link to the Sims 3 being played on a laptop with the 3rd generation Intel HD 4000 graphics core. Actual performance will be higher than what is displayed in the video because software is being used to record gameplay.
https
/www.youtube.com/watch?v=n6RiraG_168
I do recommend that another stick of 4GB RAM (a total of 8GB) should be installed since only having 4GB of RAM for Windows, Sims 3 (especially with expansions) and the graphics will likely cause low memory errors sooner or later which could cause the game to crash or the laptop to freeze up.