Answer
$ \approx -6.93$
Work Step by Step
When the surface is orientable then the flux through a surface is defined as: $\iint_S F \cdot dS=\iint_S F \cdot n dS$
where, $n$ is the unit vector.
Since, $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f(\overline(x), \overline(y), \overline(z)) AS_i$
Here, $\iint_S F(x,y,z) dS =4[f(0,0,1) +f(0,1,0) +f(1,0,0)+f(-1,0,0) +f (0,-1,0) +f(0,0,-1)]$
This gives; $\iint_S F(x,y,z) dS =4[-0.9899925-0.41614684+0.54030231+0.54030231-0.41614684-0.9899925]$
Hence, $\iint_S F(x,y,z) dS \approx -6.93$
