Find the value of $A$ if

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{e}^{2t}sin(t)dt=A+{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}2e^{2t}cos(t)dt$

$($A$)-1$

$($B$)\frac{1}{2}$

$($C$)2$

$($D$)-e^{}$

$($E$)1$