So Eq.(13) is just $\int F.n dS = \int \int div(F) dA$
So I did $div(F) = \nabla . F = y+1$, then I did $\int_2^3 \int_2^3 y + 1 dx dy = \int_2^3 y + 1 dy = .5(3^2) + 3 - (.5(2^2) + 2) = 3.5$ This multiplied by density is 1750.
This is not the answer. The answer is 29.2