Answer
45
Work Step by Step
Reading the graph,
$a_{1}=-4$
$a_{2}=-2$
$a_{3}=0$
$a_{4}=2$
$a_{5}=4$
$\displaystyle \sum_{i=1}^{5}(a_{i}^{2}+1)=$
$=((-4)^{2}+1)+((-2)^{2}+1)+((0)^{2}+1)+((2)^{2}+1)+((4)^{2}+1)$
$=17+5+1+5+17$
$=45$