Definite Integral

u know wat i guess this is a non integrable fuction ....with limits from -∞ to + ∞ means an indefinite integration.....and integral sinx/x is a non integralbe function

Assume : I(a)=2\int_{0}^{\infty}{\frac{e^{-at}sint}{t}}dt

\frac{dI}{da}=-2\int_{0}^{\infty}e^{-at}sint\: dt

\frac{dI}{da}=2\left[\frac{e^{-at}(asint+cost)}{a^{2}+1} \right]_{0}^{\infty}

\frac{dI}{da}=-\frac{2}{a^{2}+1}

I(a)=-2\, tan^{-1}a+c

as a tends to infinity integral tends to 0 : 0=-2\, tan^{-1}\infty + c

c=\pi

I(a)=-2\, tan^{-1}a+\pi

required integral : I(0)=\pi

Thanks Dubey Sir :)

Thanks Abhishek I din't see sir's profile before