6. A point on the coordinate plane whose both horizontal and vertical coordinates are integers is called an integer point. The number of integer points in the region enclosed by the parabola $y=x^{2}+1$ and the line $2 x-y+81=0$ is $\qquad$ .
6. 988 Detailed Explanation: First, solve for the intersection points of the line and the parabola, which are $(-8,65)$ and $(10,101)$. The number of integer points in the enclosed region is: $2 \times$ $(-8)+81-(-8)^{2}+2 \times(-7)+81-(-7)^{2}+\cdots+2 \times 9+81-9^{2}+2 \times 10+81-10^{2}=988$.