Because (-4,-5) and (4, 2) is a value equivalent two consecutive positive integers is bigger than 2 and smaller than 5.Thence inferred:Two integers is 3 and 4

So the sum of those two integers is:3+4=7

The length of the segment is : 

\(\sqrt{\left[4-\left(-4\right)\right]^2+\left[2-\left(-5\right)\right]^2}=\sqrt{113}\)

Since \(\sqrt{100}< \sqrt{113}< \sqrt{121}\) or \(10< \sqrt{113}< 11\), the answer is :

10 + 11 = 21