Help me find the integrands: Problem $5.$ Let $S$ be the part of the cylinder $x^2+y^2=1$ that lies between the planes $z=0$ and $z=2,$ together with its top and bottom disks. Consider the surface integral ${}_S(x^2+y^2+z^2)dS.$

If $S_1$ is the lateral surface of the cylinder, then

${}_{S_1}(x^2+y^2+z^2)dS={\displaystyle \underset{0}{\overset{2}{}}}$

If $S_2$ is the top disk, then

${}_{S_2}(x^2+y^2+z^2)dS={\displaystyle \underset{0}{\overset{2}{}}}$

$?drd=$

If $S_3$ is the bottom disk, then

$(x^2+y^2+z^2)dS={\displaystyle \underset{\phantom{}}{\overset{2}{}}}{\displaystyle \underset{\phantom{}}{\overset{1}{}}}$