Answer
$f(x+2) =x^2 + 4x + 5$;
$f(x) + f(2) = x^2 + 6$
Work Step by Step
For x = x+2
$f(x+2) = (x+2)^2 + 1$ ... square (x+2)
$= x^2 +4x +4 +1$ ... add
$= x^2 +4x +5$
_____________
For x = 2
$f(2) = (2)^2+1$ ... square 2
$ = 4 + 1$ ... add
$=5$
therefore
$f(x) + f(2) = x^2 + 1 + 5$ ... add
$= x^2 + 6$