Find the Flux of the Curl of Field F Through $\theta$

Multiple Choice

Find the flux of the curl of field F through the shell S.
-F = ( 4y + 2) i - 5xj + ( - 1) k; S: r(r, $\theta$ ) = 4 sin cos $\theta$ i + 4 sin 11ee985c_d98c_07fb_a6de_8d8f17a9f06c_TB9662_11 sin $\theta$ j + 4 cos 11ee985c_d98c_07fb_a6de_8d8f17a9f06c_TB9662_11k, 0 $\le$ $\theta$ $\le$ 2 $\pi$ and 0 $\le$ 11ee985c_d98c_07fb_a6de_8d8f17a9f06c_TB9662_11 $\le$ 11ee9522_34ee_dc81_bdb6_dd1c5864154a_TB9662_11

A) -288 $\pi$
B) 144 $\pi$
C) -144 $\pi$
D) 288