= Solution
Use the nonnegative increasing truncations $f_n=x^{-2}\mathbf1_{[1/n,1]}$. They increase almost everywhere to the specified function. On each <compact> interval the <continuous function> has equal Riemann and Lebesgue integrals, so the <fundamental theorem of calculus> gives
$$
\int f_n=\int_{1/n}^1x^{-2}\,dx=n-1.
$$
Monotone convergence yields $\int f=+\infty$. Since a nonnegative function is <Lebesgue integrable> exactly when its integral is finite, \b[this function is not <Lebesgue integrable>].
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