Let $X$ be a smooth projective variety. The map $i:X\to X\times_k X$ induced by the identity is a closed immersion. Denote its image by $\bigtriangleup$. We have $\mathcal{O}_{\bigtriangleup}=i_*\mathcal{O}$. Consider the derived category $D^b(X)$ of coherent sheaves on $X$.
How do I conclude $\mathbf{R}i_*\mathcal{O}=\mathcal{O}_{\bigtriangleup}$ ? Rather: why is $\mathbb{R}i_*(L)=i_*L$ for every line bundle on $X$?
Thanks a lot.