Evaluating Integral: $\int_0^{\pi/2} \frac{1}{y+\cos x}dx$

[RYANDTRAVERS]

How do you evaluate an integral such as:
\begin{equation}
\int_0^\frac{\pi}{2} \frac{1}{y+cosx} \, dx
\end{equation}
I was thinking whether to treat y as a constant and then integrate as such and be left with an arbitrary constant that is a function of y. This constant, f(y), should then disappear when evaluating the definite integral...?

 

[mfb]

That depends on what you want to find out. Does y have some fixed relationship to x?
Usually, y will be a constant, and the definite integral will still depend on y in the same way the integral will give different results if you replace y by different real numbers.

 

[RYANDTRAVERS]

I’ve attached my attempt at the question. Just wanted to know what you think? I’ve got a definite integral that is a function of y, I(y), and have used the substitution t=tan(x/2).