Ok, so after enabling vsync in games, it still gives me screen tearing.
Maybe I should just stick with Intel graphics for gaming anyway (for now) because there isn't that much of a performance difference between it and that dedicated AMD GPU anyway LOL
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Due to tearing issue with proprietary driver, in general open source driver is only sane choice for laptops with AMD PowerXpress. So switch to open source driver, with it you will be able to use integrated GPU (as you said there is no tearing) and launch some applications on dedicated GPU, like this: DRI_PRIME=1 steam (dGPU will be power up/down automatically).
For latest open source driver you will need Ubuntu or Kubuntu 15.10.
This also could be useful:
For hardware accelerated video decoding in VLC install VA-APi driver for your Intel GPU (i965-va-driver package) and choice VA-API in VLC settings (and OpenGL video output). You also could install gstreamer1.0-vaapi for hardware accelerated video decoding in Firefox.
In latest Radeon open source driver in (K)Ubuntu 15.10 there is OpenGL 3.3. To get OpenGL 4.1 (some games need it) add Padoka PPA to you system, and do system update. Don't forget to do ppa-purge before upgrade to 16.04 (otherwise you get broken system after upgrade). With this PPA you also can install mesa-opencl-icd to get OpenCL 1.1 (without image processing support yet unfortunately).