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Given Question - Let $f:[0,5] \to \mathbb{R}$ be a function defined by $$f(x) = 2x^{2} + 3x + 5, \quad x \in [0,5].$$ Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match. # Solution Let $f:[0,5]\to\mathbb R$ be $f(x)=2x^{2}+3x+5.$ ## 1. Riemann integrability by the continuity/Darboux criterion $f$ is a polynomial, hence continuous on ____ _______ _______ _________ _______ ____ __________ __________.
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