Let G = (V(G),E(G)) be a simple graph and denote by du the degree of the vertex u ∈ V(G). Using a geometric approach, I. Gutman introduced a new vertex-degree-based topological index, defined as SO(G) = (du)2 + (dv)2, uv∈E(G) and named Sombor index. It is a molecular descriptor with an impressive research activity in recent years. In this paper we propose and initiate the study of a family of topological indices, also conceived from a geometrical point of view, called irregularity integral Sombor indices, that generalize the Sombor index. Also, we study the application of these indices in QSPR/QSAR research.