  We remark a variant of the existence part of the fundamental theorem of
calculus, which, together with the Lebesgue differentiation theorem, constitute
a new proof that every Riemann-integrable function on a compact interval having
limit everywhere on the interior is almost everywhere continuous with respect
to Lebesgue measure. The proof is intended as a new connection between Lebesgue
differentiation theorem and Lebesgue criterion of Riemann integrability.
