\[\int_{0}^{\pi /2}{{{e}^{x}}\sin x\,dx=}\] [Roorkee 1978]

• A. \[\frac{1}{2}({{e}^{\pi /2}}-1)\]
• B. \[\frac{1}{2}({{e}^{\pi /2}}+1)\]
• C. \[\frac{1}{2}(1-{{e}^{\pi /2}})\]
• D. \[2({{e}^{\pi /2}}+1)\]