Why Gauss' law uses different sides for wire vs plane sheet

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Application of Gauss' law -- some doubts

Homework Statement



Revered Members,
I have attached images of applications of Gauss' law namely 1) Electric field due to an infinitely long charged wire and 2) Electric field due to an infinite charged plane sheet.
In both cases Gaussian surface is cylinder.
In the first case, the electric flux is found for curved surface and it has been done for only side that is right side of cylinder in this case
In the second case, the electric flux is found for plane caps but it has been done for both the left plane cap and right plane cap.
My doubt is , why we are doing for only one side for the curved surface and for both sides in the case of plane caps?
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Homework Equations





The Attempt at a Solution



 

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My fourth attachment.
 

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