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