This message was posted on behalf of Intel Corporation
In regard to your question, there is no option to upgrade the graphics controller on those chipsets.
In order to use Intel® HD graphics 3000 or higher, you need to replace the processor for one that has that type of graphics controller, for example to use the Intel® HD graphics 3000 you need a second generation processor and those are not compatible with those chipsets, as you can confirm on the following links:
Compatible processors for chipset G31:
Compatible processors for chipset G33:
Any questions, please let me know.