>>286 補足追加
>https://en.wikipedia.org/wiki/Riemann_integral
>Riemann integral
>Integrability
>A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is continuous almost everywhere (the set of its points of discontinuity has measure zero, in the sense of Lebesgue measure). This is the Lebesgue-Vitali theorem (of characterization of the Riemann integrable functions).

この”A bounded function on a compact interval [a, b]”
「コンパクト区間[ a , b ]上の有界関数」

この有界の条件は、抜かさない方が良いようですね
抜かすと、証明が複雑になる（反例がある？）