The value of integral \(\mathop \smallint \limits_0^2 \mathop \smallint \limits_0^{\rm{\ \ \ \ x}} {{\rm{e}}^{{\rm{x}} + {\rm{y}}}}{\rm{dydx}}\) is

• A. \(\frac{1}{2}\left( {{\rm{e}} - 1} \right)\)
• B. \( \frac{1}{2}{\left( {{{\rm{e}}^2} - 1} \right)^2}\)
• C. \(\frac{1}{2}\left( {{{\rm{e}}^2} - {\rm{e}}} \right)\)
• D. \(\frac{1}{2}{\left( {{\rm{e}} - \frac{1}{{\rm{e}}}} \right)^2}\)