Spicy Limits and Integrals!

Calculus Level 4

$\begin{cases} \Omega_1 = \displaystyle \int_0^1 \sin^{-1} \left( \dfrac{x}{\sqrt{1+x^2}} \right) \mathrm{d}x \\ \Omega_2 = \displaystyle \int_0^1 \cos^{-1} \left( \dfrac{x}{\sqrt{1+x^2}} \right) \mathrm{d}x \\ \Omega_3 = \displaystyle \lim_{n \to \infty} \left( \dfrac{1}{n+1} + \dfrac{1}{n+2} + \ldots + \dfrac{1}{2n} \right) \end{cases}$

Define $\Omega_1, \Omega_2, \Omega_3$ as of above. Then which one of the following choices is correct?

\Omega_1 + \Omega_2 + \Omega_3 = 4

\Omega_1 + \Omega_2 + \Omega_3 = \ln(2)

\Omega_1 + \Omega_2 = \Omega_3

\Omega_1 + \Omega_2 + \Omega_3 = 0

\Omega_1 + \Omega_3 = \Omega_2

\Omega_2 + \Omega_3 = \Omega_1

\Omega_1 + \Omega_2 + \Omega_3 = 1

\Omega_1 + \Omega_2 + \Omega_3 = \ln(4)