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$Goal: we will prove that if $ f $ and $ g $ are two Riemann integrable functions then \[ \int_{a}^{b}(f(x)+g(x)) d x=\int$

$Using the property that a Riemann integral can be written as the limit of a Riemann sum, prove that \( \int_{a}^{b}(f(x)+g(x)$

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please label each section and show work clearly. will upvote thank you      Goal: we will prove that if f and g are two Riemann integrable functions then ?ab?(f(x)+g(x))dx=?ab?f(x)dx+?ab?g(x)dx. First, we will prove first that f+g is Riemann integrable and then prove the above equality. 2.1 Show that ?P partition of [a,b],U(f+g,P)?L(f+g,P)?[U(f,P)?L(f,P)]+[U(g,P)?L(g,P)]. 2.2 Using 2.1 and the definition of Riemann integrability, prove that f+g is Riemann integrable.  Using the property that a Riemann integral can be written as the limit of a Riemann sum, prove that ?ab?(f(x)+g(x))dx=?ab?f(x)dx+?ab?g(x)dx.

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