Answer
The consecutive integers are
$\{ 2,5,10,17,26,37\}$
and the sum is $=97$.
Work Step by Step
The given expression is $n^2+1$.
Plug $n=1$.
$=1^2+1$
$=1+1$
$=2$.
Plug $n=2$.
$=2^2+1$
$=4+1$
$=5$.
Plug $n=3$.
$=3^2+1$
$=9+1$
$=10$.
Plug $n=4$.
$=4^2+1$
$=16+1$
$=17$.
Plug $n=5$.
$=5^2+1$
$=25+1$
$=26$
Plug $n=6$.
$=6^2+1$
$=36+1$
$=37$.
Sum of the all values.
$=2+5+10+17+26+37$
$=97$.
