Currently I faced a problem where I automatically logged on to Kali Linux using gnome-fallback session. This made me think that maybe my graphic driver is not installed thus results in Kali Linux using gnome-fallback session as the default session when logging in.

However, I am pretty sure that this Intel 3rd Generation graphics are  supported out of the box by most Linux distros and i already reinstalled using the command sudo apt-get install xserver-xorg-video-intel.
I also install mesa-utils using sudo apt-get install mesa-utils but nothing changed even after I rebooted my notebook.

After a quick google search session, I stumbled upon a solution and here it is:

To use gnome session as default, you'll have to open up terminal and type this in as root:

dbus-launch gsettings set org.gnome.desktop.session session-name 'gnome'

This will set your default session to gnome instead of gnome-fallback. This, however needs your graphic card to support 3D acceleration and driver properly installed.

To check whether the gnome-fallback not in use anymore, you can type this command in terminal and see the output.

gsettings get org.gnome.desktop.session session-name

Mine below is showing 'ubuntu' and not gnome-fallback, so I'm good. If your output is gnome-fallback, you'll have to work around and tweak some more.