In this manuscript we denote a unit disc by $\mathbb{D}=\{z\in \mathbb{C} \mid |z|<1\}$ and a semi plane as\\ $\mathbb{P}=\{s\in\mathbb{C}\mid \Re(s)>\frac{1}{2}\}$. We denote, $\mathbb{R}_{\geq 0}=\{x\in \mathbb{R}\mid x\geq 0\}$ and $\mathbb{R}_{\geq 1}=\{x\in \mathbb{R}\mid x\geq 1\}$. Considering non negative real axis as a branch cut, we define a map from slit unit disc to the slit plane as $s:\mathbb{D}\setminus \mathbb{R}_{\geq 0}\to \mathbb{P}\setminus\mathbb{R}_{\geq 1}$ defined as $s(z)=\frac{1}{1-\sqrt{z}}$ which is proved to be one-one and onto. Next, we define a function $f(z)=(s-1)\zeta(s)$ where $s=s(z)$ and both $s(z)$ and $f(z)$ are proved to be analytic in $\mathbb{D}\setminus \mathbb{R}_{\geq 0}$. Next we prove that $s=s(z)$ is a conformal map. We also show that $f$ is continuous at $0$. Using Cauchy's residue theorem to a keyhole contour and Lebesgue's dominated convergence theorem along with Schwarz reflection principle, we prove that, $$\int_{-\infty}^\infty \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt=0$$ This settles the Riemann Hypothesis because this relation is an equivalent version of Riemann Hypothesis as proved by Balazard, Saias and Yor [1].