I responded to a thread yesterday where someone asked a very similar question, but had a $600 budget. The best out there I could find was this laptop at microcenter, but you would have to go to a physical store to get one.
http://www.microcenter.com/product/450764/Aspire_E5-572G-72M5_156_Laptop_Computer_-_Midnight_Black
Honestly though, if you do find a laptop that has an i5 for the price you are looking for, it will be an older CPU and the screen is going to be 1366x768 resolution (essentially 720p).
The newest integrated graphics right now is the Intel HD 6000 series, but its very new. When you are looking at laptops, compare them based on the specific model number of the CPU to know where you stand on graphics. But you have been warned, they will not be on high setting and you will run at about 30 fps at the start of the game (not even gonna speculate where dismal frames you will get during team fights).