fInt = Integrate[((1 - (1/((1 +
         s*y*(0.5*Sqrt[1/[Lambda]])^([Alpha]*[Epsilon]))^(M -
         K + 1))))*(1 -
         Exp[-[Lambda]*y^(-2/[Alpha])]))*(y^((-1/[Alpha]) - 1)),
         {y,r0^(-[Alpha]), 0},
         Assumptions ->  r0 > 0 &&  [Epsilon] > 0 &&  [Lambda] > 0 ]