Integration within constructive, especially intuitionistic mathematics in the sense of L. E. J. Brouwer, slightly differs from formal integration theories: Some classical results, especially Lebesgue's dominated convergence theorem, have tobe substituted by appropriate alternatives. Although there exist sophisticated, but rather laborious proposals, e.g. by E. Bishop and D. S. Bridges , the reference to partitions and the Riemann-integral, also with regard to the results obtained by R. Henstock and J. Kurzweil , seems to give a better direction. Especially, convergence theorems (...) can be proved by introducing the concept of “equi-integrability”. (shrink)