f\left( x \right) - x - 1 = \int {\left( {\sum\limits_{n \ge 2} {\frac{{n \cdot s_{n - 1} x^{n - 1} }}{{n!}}} } \right)dx} + \int {\left( {\sum\limits_{n \ge 2} {\frac{{n\left( {n - 1} \right)s_{n - 2} x^{n - 1} }}{{n!}}} } \right)dx}