@milkywayy,, Your HP system has graphics drivers installed that have been customized by HP specifically for your system. If you update them with the generic Intel HD Graphics drivers, you will loose the HP customizations which may cause your system to not function the HP intended it to.
If you do want to take the risk of installing generic drivers, I would recommend creating a restore point prior to the installation.
Here are the steps you need to use to install the generic drivers.
1. Login with administrator privileges
2. Open Control Panel
3. Open Device Manager
4. Click on "Display adapters"
5. Double click "Intel HD Graphics"
6. Click on the "Driver" tab
7. Click on "Update Driver" button
8. Click on "Browse my computer for driver software"
9. Click on "Let me pick from a list of device drivers on my computer"
10. Click on "Have Disk" button
11. Click "Browse"
12. Navigate to the folder that you unzipped the Beta Intel HD Graphics driver to
13.Navigate to the Graphics sub-folder
14. Double click the igdlh64.inf or igdlh.inf file <-- depends on if you have 32 or 64 bit OS
15.Click "OK"
16. Click "Next"
Driver should now be installing.
17. If successful, click "Close"
Reboot.