The question is related to integration and we have to used the following formula
[tex] \frac{1}{b-a}\int\limits^a_b {f(x)} \, dx [/tex]
[tex] \frac{1}{\pi /2 -0}\int\limits^0_{\pi/2} {e^{sin t}cos t } \, dt [/tex]
[tex] = \frac{2}{\pi}(e^{sin t})_{0}^{ \pi /2} [/tex]
[tex] =\frac{2}{\pi}(e^{sin(\pi/2)} -e^{sin0}) [/tex]
[tex] =\frac{2}{\pi}(e -1) [/tex]
