Assuming you've learned the h/3 version of Simpson's rule:
h=(2-1)/4 = 1/4
So the x-values used are 1, 1.25, 1.5, 1.75, 2
So the y-values used are 1, 4/5, 2/3, 4/7, 1/2
So the approximate value of the integral is:
(1/4)/3 [1 + 1/2 + 4 (4/5 + 4/7) + 2(2/3) ]