  The concept of integral as an inverse to that of derivation was already
introduced for rings and recently also for lattices. Since semirings generalize
both rings and bounded distributive lattices, it is natural to investigate
integration in semirings. This is our aim in the present paper. We show
properties of such integrals from the point of view of semiring operations.
Examples of semirings with derivation where integrals are introduced are
presented in the paper. These illuminate rather specific properties of such
integrals. We show when the set of all integrals on a given semiring forms a
semiring again.
