Abstract: For the Fresnel-type integral which is difficult to be solved by real function theory,the Dirichlet test is first applied to prove its convergence.Then,the general convergence result of Fresnel-type integral with x^n－2 or x^m are given by applying the circulatory integral method and Cauchy integral theorem.

Key words: Fresnel type integral, Dirichlet test, circulatory integral method, Cauchy integral theorem