Is it legal to include another person's result in my research paper? Is it legal to include another person's result in my research paper? 

For instance:

Theorem (Name of the author): Statement

Proof. The proof of this appeared in [1].
Isaac Newton said, "If I have seen further, it is by standing on the shoulders of giants." Research would grind to a halt if each scientist had to start from "scratch."

So the question becomes, "How should I use the work of others?"

The answer: By citing their published work.  Since the number of times a publication has been cited is often used to measure its impact, this is both fair and ethical.