at line $y=-2$, we have $(5,-2)(6,-2)(1,-2)(0,-2)$ $\Rightarrow 4$ points

at line $y=-1$, we have $(4,-1)(5,-1)(6,-1)(2,-1)$ $(1,-1)(0,-1) \Rightarrow 6$ points

at line $y=0$, we have $(0,0)(1,0)(2,0)(3,0)(4,0)$ $(5,0)(6,0) \Rightarrow 7$ points

at line $y=1$, we have $(1,1),(2,1),(3,1),(4,1),(5,1)$ i.e. 5 points

symmetrically

at line $y=-5$, we have 5 points

at line $y=-4$, we have 7 points

at line $y=-3$, we have 6 points

So Total integral points $=2(5+7+6)+4$

$$ =40 $$