Keeping yellow belly turtles as pets is a walk on the wild side whether they are captive raised or wild capture. When considering any animal that is descended from wild animals or a wild capture, make sure to check the laws in your specific area for your specific species. Laws are different for a variety of reasons including controlling the spread of disease, protecting the native species that might be affected by crossbreeding from an escaped pet, or maintaining proper import/export restrictions. Most species are on the LC or Least Concern of extinction list, but it is fair to say the more research you do prior to getting your pet, the safer and happier your pet will be.
Being semi-aquatic means you will need to provide water and land for a new turtle pet. A good rule is to choose or build an enclosure that is three times the width and six times the length of the shell of the pet. If there will be more than one pet per enclosure, larger accommodations will be needed. If the pets are mature adults the possibility of mating can easily occur and may go unnoticed until eggs or hatchlings appear on the scene. They will need a UV-B light for basking in order to completely dry out at times, natural sun is best but is not always available.
In turtle terms, their lifespan is relatively short, being only around 15-25 years. In pet terms, however, this means a turtle pet is a long obligation, not a short-term whim. A well cared for turtle pet can feasibly outlive its owner so it is important to make arrangements for them along with other assets.
Feeding is an easy process since yellow-bellied turtles are omnivores and will eat plant or animal matter as well as carrion in the wild if no other food source is available. Young turtles need more protein for growth and will enjoy crickets, mealworms, earthworms, or other purchased reptile/turtle food. Mature turtles tend to enjoy more plant foods such as berries, fruits, vegetables, and canned turtle food that is generally cubed fruits and vegetables. If feeding fruits and vegetables, be aware to remove uneaten food to avoid soiling the water supply.
Most turtles with a single or double-hinged plastron (lower shell) are generally timid in nature and prefer to hide rather than confront danger. This does not exclude them from an occasional nip if they are pushed or scared, but it should be a nip of small consequence unlike the bite from their aggressive cousins, the snappers. Yellow belly turtles can be lifelong companions and should be treated with that respect.