My problem is updating Core and GLSL version of OpenGL. I installed newest Intel drivers for my HD 4400 and still got GLSL 1.30. Thing is, this GPU should support OpenGL/GLSL 4.0. No matter what I do, it seems it can't be upgraded and glxinfo still displays 1.30 GLSL. Any help with this from anyone who had similar problem?
glxinfo reporting GL 3.0/GLSL1.30 is fine for this GPU. You are using the Mesa3D open source OpenGL implementation. This does currently support OpenGL up to version 3.3. However, it only does support modern GL for core profiles only (and which is the only profile they are required to proovide, as by the spec). In compatibiliy mode, it is limited to GL 3.0 / GLSL 1.30 - and that is what you see here.
Old versions of glxinfo do not know about core profiles at all, and are limited to compatibility/legacy contexts. More recent versions of glxinfo will report both. So for an Intel HDxxxx GPU on Linux, you will get an output similiar to
$ glxinfo | grep -i opengl
OpenGL vendor string: Intel Open Source Technology Center
OpenGL renderer string: Mesa DRI Intel(R) Ivybridge Mobile
OpenGL core profile version string: 3.3 (Core Profile) Mesa 10.0.1
OpenGL core profile shading language version string: 3.30
OpenGL core profile context flags: (none)
OpenGL core profile profile mask: core profile
OpenGL core profile extensions:
OpenGL version string: 3.0 Mesa 10.0.1
OpenGL shading language version string: 1.30
OpenGL context flags: (none)
OpenGL extensions: