There is a typo, for there are no such consecutive integers.  I am guessing
that the 25/56 should have been 15/56.  I will assume that.

Smaller integer = x
Larger integer = x+1

                   

Multiply through by LCD of 56x(x+1), written as 

       

     
   
             56(x+1) + 56x = 15x(x+1)

            56x + 56 + 56x = 15x² + 15x

                 112x + 56 = 15x² + 15x
                         0 = 15x² - 97x - 56
                         0 = (x - 7)(15x + 8)
             
                       x - 7 = 0;   15x + 8 = 0
                           x = 7        15x = -8
                                          x = 

Ignore the fraction answer.

Thus the integers are x = 7 and x+1 = 8

Edwin