In the words of the authors, they ``have defined a descriptive Denjoy type integral which solves the so-called coefficients problem for trigonometric series whose behaviour is known only almost everywhere''. More precisely, a function \(f\) is said to be \(D_2\) integrable on \([a,b]\) if there is a continuous function g which is smooth in \((a,b)\) such that \(g\) satisfies generalized absolute continuity of second order with existing one-sided approximate derivatives of \(g\) at the endpoints of \([a,b]\) and the second approximate derivative of \(g\) equals \(f\) almost everywhere. Then the approximate derivative of \(g\) is the primitive of \(f\), whereas \(g\) is the second primitive of \(f\). Note that the integral is not symmetric as in many other cases. Under certain conditions, the Fourier series with respect to the \(D_2\) integral converges allowing an exceptional set of measure zero.