To prove $| S(f,P,T) - S(g,P,T) | \leq M(b-a)$
Question : Let $[a,b] \subseteq R$ be a non degenerative closed bounded interval and let $f,g :[a,b] \rightarrow R$ be functions .Suppose that there is some M belonging to N(natural numbers) such that $|f(x)-g(x)| \leq M$ for all $x$ in $[a,b]$ .Let P be a partition of $[a,b]$ and let T be a representative set of P .Prove that $| S(f,P,T) - S(g,P,T) | \leq M(b-a)$
ATTEMPT
Firstly is this correct ? If this proof is correct ,this is for partition with equal widths ,what if the widths are not equal then how will proof be modified .Thanks