1st integer = n
2nd integer = n+1

    n²+(n+1)² = 41
n²+(n+1)(n+1) = 41
n²+(n²+n+n+1) = 41
 n²+(n²+2n+1) = 41
   n²+n²+2n+1 = 41
     2n²+2n+1 = 41
    2n²+2n-40 = 0
Divide through by 2
      n²+n-20 = 0
Factor:
    (n+5)(n-4) = 0     <--- that's the answer to the second part

Use the zero-factor property

  n+5=0;  n-4=0
    n=-5;   n=4

Since they are consecutive NEGATIVE integers, we ignore
the positive answer.

1st integer = n = -5
2nd integer = n+1 = -5+1 = -4

Edwin