Line integral comparison, multivariable calculus

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I have a question on line integrals. If $C_1$ and $C_2$ are the circular disks inscribing and circumscribing $R$, ($R= [−r,r]×[−r,r]$) does it mean the line integral of $e^{−(x^2+y^2)}$ over $C_1$ is smaller than $R$ smaller than $C_2$ because the area of $C_1$ is smaller than $R$ smaller than $C_2$? Can I compare line integrals using their area bounded by the curve if they are in $2D$?