My eleventh integral problem

Calculus Level 5

$\large \displaystyle \int_{0}^{\pi/2} e^{x} \cos^{2} x \, dx$

It is given that the above integral can be expressed in the form $\large \dfrac{a e^{{b \pi}/{c}}-d}{f}$ where $a, b, c, d, f$ are positive integers, $\gcd(a,f) = \gcd(b,c) = 1$ .

Find the value of $a+b+c+d+f$ .