Similarities and differences between some of the integrals of the 20th century

In A Half-Century of Mathematics written in 1951, Hermann Weyl aims to account for the mathematics of the first half of the twentieth century. Regarding Lebesgue's integral and measure theory he stares that: "I must mention the, in all probability final, form given to the idea of integration by Lebesgue at the beginning of our century." However, there exist over a hundred integrals to date so Weyl's comment regarding the final form of the integral seems rather stringent. Our goal here is to compare two integrals in particular, Denjoy’s and Daniell’s, and to analyse the conceptual change that took place after the introduction of Lebesgue's integral that made them possible