As the title says even when I play lightweight and or old games even with vsync on with intel's integrated graphics my notebook's fan is being too loud
When buying a new notebook most people only care about the CPU, GPU, RAM and Storage brand, model and performance. Not many care to look for info about its cooling system.
As dotas1 mention already, notebooks (new, old, cheap or even many expensive ones) usually come with a crappy cooling solution. A solution which at best, will allow you to keep the cpu and gpu from metling down the rest of the system. And of course always at the cost of high fan noise.