Firstly,the article theoretically expounds the superiority of Lebesgue Integral,then through the detailed cases analyzes its superiority shown in the practical application compared to Riemann Integral.

Their properties and the connection with Lebesgue integral sum and integral are studied.

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

The relations between the Lusin theorem and the natural disposition theorem of the Lebesgue measurable functions are discussed in this paper,according to the almost every point of the n-dimension Lebesgue measurable set being the entire dense spot and the Lusin theorem.