Evaluate: $$\phi(y) = \int_0^\frac{\pi}{2} \frac{1+y\sin^2(x)}{\sin^2(x)} dx $$
After applying the Leibniz formula, the indefinite integral of $d\phi(y)$ comes out to be: $$\int d\phi(y)=\frac{\pi}{2}\int dy$$ i.e.
$$\phi(y) = \frac{\pi}{2}y+c$$
Now I am stuck in finding the value of $c$. On putting $y=0$ the integral does not converges! How can I find the complete function? Is it possible or am I doing something wrong. Please help.
Thank you