How do I install intel integrated graphics controller?

What you ran was lspci | grep -i vga that effectively gives you that "video card". You are already using the appropriated drivers for your system. If you want to see the kernel driver you should use lspci -knn | grep -A2 VGA

lspci -knn | grep -A2 VGA 
03:00.0 VGA compatible controller [0300]: Advanced Micro Devices, Inc. [AMD/ATI] RV515 [Radeon X1300/X1550] [1002:7146]
    Subsystem: VISIONTEK Device [1545:2352]
    Kernel driver in use: radeon
                          ^^^^^^

As you can see, that is my "driver" for my dedicated video card. In your case it shows like that since recently Intel now includes GPU properties in their CPU. So the output is correct.

If you are having problems with your current drivers, is probably a bug, and as such it should be reported in LaunchPad. In AskUbuntu is there a guide to do so.

Here are the ways to install Intel Graphics Card Driver

1. If you are using Ubuntu 12.10 or higher, then you don't have to worry, as Intel has
 released a software for Linux system which will scans your graphics card and try to 
 install appropriate graphics driver. Please refer following link:

https://01.org/linuxgraphics/downloads/2013/intelr-linux-graphics-installer-version-1.0.2

2. If you are using Ubuntu 12.04 or less then you can always install you graphics driver
by running these command:

    $ sudo apt-get update
    $ sudo apt-get install xserver-xorg-video-intel

3. You can also give a try to this:

    $ sudo (jockey-gtk &)
As it will scan all your available drivers and try to install the missing one.

4. If nothing works then finally install latest driver by following these steps:

• Open Ubuntu Software Center.
• From the top-level menu, select Edit | Software Sources ... .
• Select the Other Software tab.
• Click the Add ... button.
• Enter the following: deb https://download.01.org/gfx/ubuntu/12.04/main
• Click the +Add Source button.
• Provide your user password when requested.
• Click the Close button.

• Update and install by executing following commands:

  $ sudo apt-get update
  $ sudo apt-get install xserver-xorg-video-intel
  

Hope it will work for you!