Prove this integral is analytic Let $\phi$ be a continuous (complex valued) function on the real interval [−1, 1] inside C, and deﬁne
$$f(z)=\int_{-1}^1\frac{\phi(t)}{t-z}dt$$
Show that f is analytic on C less the interval [−1, 1].
I thought about CR equation to prove analytic but the function is not of the form $f(z) = u(x, y) + iv(x, y)$

Hint:
$$u(x,y)=\Re\int_{-1}^1\frac{\phi(t)\,dt}{t-z},\\v(x,y)=\Im\int_{-1}^1\frac{\phi(t)\,dt}{t-z}.$$
