If an integer is added to its square, the sum is 90.

Let an integer be x.

Then according to question

$x+x^{2}=90$

$x^{2}+x-90=0$

$x^{2}+10 x-9 x-90=0$

$x(x+10)-9(x+10)=0$

$(x+10)(x-9)=0$

$(x+10)=0$

$x=-10$

Or

$(x-9)=0$

$x=9$

Thus, an integer be $-10,9$