Answer
$f(x)=e^{x}+2\displaystyle \sin x-\frac{2x(e^{\pi/2}+4)}{\pi}+2$
Work Step by Step
$f''(t)=e^{x}-2\sin x$
Using the antiderivatives table,
$f'(x)=e^{x}+2\cos x+C$
Using the antiderivatives table,
$f(x)=e^{x}+2\sin x+Cx+D$
$\left\{\begin{array}{llll}
f(0)=3 & \Rightarrow & 1-0+0+D=3 & \\
& & D=2 & \\
f(\pi/2)=2.6 & \Rightarrow & & e^{\pi/2}+2(1)+C(\pi/2)+2=0\\
& & & C(\pi/2)=-(e^{\pi/2}+4)\\
& & & C= -\dfrac{e^{\pi/2}+4}{\pi/2}
\end{array}\right.$
$f(x)=e^{x}+2\displaystyle \sin x-\frac{e^{\pi/2}+4}{\pi/2} \cdot x+2$
$f(x)=e^{x}+2\displaystyle \sin x-\frac{2x(e^{\pi/2}+4)}{\pi}+2$
