(20) Let $f \in L[a, b]$. For $x \in (a, b)$, define $G(x)$ by $G(x) = \int_a^x f$. Prove or give a counterexample: G is continuous on $(a, b)$.
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We are given that f ∈ C[a,b], which means that f is continuous on the closed interval [a,b]. This implies that f is also continuous on the open interval (a,b), since continuity on a closed interval implies continuity on any subinterval. Show more…
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