For \(f(x)=\int \frac{\mathrm{e}^x}{\sqrt{4-\mathrm{e}^{2 x}}} \mathrm{~d} x\), if the point \(\left(0, \frac{\pi}{2}\right)\) satisfies y = f(x), then the constant of integration of the given integral is:
1
\(\frac{\pi}{2}\)
2
\(\frac{\pi}{3}\)
3
\(\frac{\pi}{6}\)
4
0