Can I programming OpenGL4+ in a card that support 2.1 only?

This is the OpenGL version I have:

Video Card Vendor:    Intel
Renderer:             Intel(R) HD Graphics
OpenGL Version:       2.1.0 - Build
GLU Version: Microsoft Corporation

I’d like to know if I can programing in OpenGL 4+. Because I cannot update my card.

Unless your card and driver supports OpenGL 4+ you cannot use it. Most likely in your case you are stuck with GL 2.1. You need to get a more recent AMD or NVIDIA GPU (I don’t think Intel has any card/driver that supports GL 4.x yet) and get the latest drivers. Radeon HD5000+ and GeForce 400+ have GL 4.x support.

Can you tell us the exact model of your CPU?
If it is a third generation Intel Core i-processor (with HD2500/HD4000 graphics card), then yes.
Otherwise - NO!