-- deleted --

f(x + 1)  =  x² - 3x + 2   --->   f(x + 1)  =  (x - 2)(x - 1)   --->   f(x)  =  (x - 3)(x - 2)

f(x)  =  0   --->   (x - 3)(x - 2)  =  0   --->   x  =  2  or  x  =  3

Sum  =  2 + 3  =  5 

That is another really tricky little question.

thanks Geno :)