The integral of the arc length squared

Question

Given the length of a parametric curve, $l=\int_{\theta_1}^{\theta_2} \sqrt { ( { {dx} \over {d \theta}} )^2 + ( { {dy} \over {d \theta}} )^2} d\theta $. Does $l^2=\int_{\theta_1}^{\theta_2} ( { ( { {dx} \over {d \theta}} )^2 + ( { {dy} \over {d \theta}} )^2} )d\theta $ ? Is there a simple explanation why $ g = \int f dx $, $g^2 $ doesn't equal $\int f^2 dx$?