$a,b$ integral $\implies$ $a+b$ integral

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I'm sure it's just silly thing. I'm reading Fulton's algebraic curves book and I don't understand this phrase of this proof:

I didn't understand why according to the proposition we have $a\pm b,ab$ integral over $R$.

Proposition

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In the proposition, take $R' := R[a, b]$ to be the subring containing $R[a + b]$ (or $R[ab]$).