Suppose $f$ has absolute minimum value $m$ and absolute maximum value $M.$ Between what two values must ${\displaystyle \underset{4}{\overset{6}{}}}f(x)dx$ lie? $($Enter your answers from smallest to largest.$)$

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Which property of integrals allows you to make your conclusion?

If $mf(x)M$ for $axb,$ then $m(b-a){\displaystyle \underset{a}{\overset{b}{}}}f(x)dxM(b-a).$

If $f(x)0$ for $axb,$ then ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx0.$

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=-{\displaystyle \underset{b}{\overset{a}{}}}f(x)dx$

${\displaystyle \underset{a}{\overset{c}{}}}f(x)dx+{\displaystyle \underset{c}{\overset{b}{}}}f(x)dx={\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$

${\displaystyle \underset{a}{\overset{a}{}}}f(x)dx=0$