The study of an organism that lived 10 million years ago would most likely fall under which two branches of natural science?

The two branches this would likely fall under are:

Paleontology, which is the scientific study of life existent prior to the Holocene Epoch era. Using biochemistry, mathematics and engineering, paleontologists are able to discover much about of the evolution of life, almost all the way back to when Earth became capable of supporting life, about .

Biology, which is the study of life and living organisms, including their structure, function, growth, evolution, distribution, and taxonomy.