How to solve

Estimate ${\displaystyle \underset{0}{\overset{3}{}}}f(x)g^{\text{'}}(x)dx$ if $f(x)=x^2$ and $g(x)$ has the values given in the following table. $($Note that one way to estimate the integral would be to assume that $g(x)$ is a constant, or a linear function between the two endpoints; generate a more accurate estimate than that by using the provided table of data.$)$

$\backslash$table$[[x,0,0\mathrm{.}5,1,1\mathrm{.}5,2,2\mathrm{.}5,3],[g(x),2\mathrm{.}7,2\mathrm{.}9,3\mathrm{.}5,4,4\mathrm{.}14\mathrm{.}6,5\mathrm{.}5,]]$

${\displaystyle \underset{0}{\overset{3}{}}}f(x)g^{\text{'}}(x)dx=$

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