Given the below trigonometric series:
$1 + \sum_{n=1}^{\infty} \frac{2}{1+n^{2}}\cos (nt)$
Where $f(t)$ is the value of the series.
Can I then deduce that $\int_{-\pi}^{\pi} f(x) dx$ is $2\pi$? I ask because the series for $f(t)$ looks like a fourier series and I can then recognize that $1 = \frac{1}{2} \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) dx$.
?