It is a well-known result of convex analysis that two lower semicontinuous convex functions with the same subdifferential mappings are equal up to an additive constant. This property, however, is not true for nonconvex functions using the Clarke subdifferential or related notions, even if Lipschitz continuity is assumed. That means that in the general case it is not possible to determine exactly the function \(f\) by integration of their subdifferential \(\partial f\). In the paper, the authors introduce the notion of convexly subdifferential similarity. It is proved that two functions defined over an open convex set of a Banach space differ by an additive constant if and only if they are convexly subdifferentially similar. Some assertions regarding convex functions and d.c.-functions are obtained as conclusions. Moreover, the authors point out that the introduced concept allows also the integration of so-called primal lower nice functions (introduced by Poliquin 1991 as a class of functions which are completely characterized by their subdifferentials). Some results of Poliquin regarding the integration of special compositions of functions are extended in the last sections of the paper.