Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } ( x , y , z ) = y ^ { 2 } \mathbf { i } + x \mathbf { j } + z \mathbf { k }$ and S is the part of the surface $z = x + y ^ { 2 }$ that lies above the rectangle $( 0 \leq x \leq 1,0 \leq y \leq 2 )$ and has upward orientation.