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Determine which expression represents the length of the curve $f( x ) =\sqrt x$ from $x = 1$ to $x = 2$.

A

$\int _{ 1 }^{ 2 }{ \sqrt { 1+\cfrac { 1 }{ 4x }} dx } $

B

$\int _{ 1 }^{ 2 }{ \sqrt { 1+\cfrac { 1 }{ x } } dx } $

C

$\int _{ 1 }^{ 2 }{ \sqrt { 1+4x } dx } $

D

$\int _{ 1 }^{ 2 }{ \sqrt { 1+x } dx } $

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