Prove that, if a function is continuous in closed interval then it is also bounded and its attains

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if f is continuous in [ a b] ,f attains it's bounds

Continuity of Open and Closed Intervals! (Calculus 1)

f is continuous on a closed interval [a,b] , then it attains it's bounds at least once in [a,b] .

If f(x) is continuous in [a,b] then || f(x) is bounded in [a,b] | f(x) attains its bounds supremum..

If a function is continuous on closed bounded interval then it will attain the supremum and infimum

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Continuous Functions are Riemann Integrable

Proof that a continuous function on a closed interval is uniformly continuous