What are the chances of surviving stage 2 cancer found in the intestine?

You need more precise information to know the risks.  There's a small intestine and large intestine.  The large intestine is the same thing as the colon.  The small intestine is upstream from the colon.  There's several different types of cancers that can occur in the small intestine, and there's fairly large differences in the risks, depending on the cancer type.   

But for all cancer types, finding the cancer at stage 2 is generally pretty good.  At stage 2 there is a risk that cancer cells have spread to nearby lymph tissues.  If the tumor is in a location where surrounding tissues can easily be removed, there's still a chance that all of the cancer can be removed surgically. 

This is a question for your doctor.  The colon isn't the same as the intestines, so it depends where it was found.  For example, there are several cancers that are found in the small intestine.  Some are a lot more aggressive than others.  If you're asking because of a friend or relative, you need to find out the exact name of the cancer.   Then you can use reliable sources like the NCI or NIH to google the general prognosis.

Very good news. Stage 2 means it hasn't spread far, if at all.

Stage II tumors have survival rates ranging from 55 to 80 percent -- depending on the exact spread.