Help me please.

Prove or disprove:
1.
$\displaystyle Re \left(\int_{\Gamma} f(z)dz\right)=\int_{\Gamma}Re f(z)dz$

2.

Prove that if $\displaystyle f(z)dz$- it is analytical function in C , then $\displaystyle \overline{ f(\overline{z})}$ also analytical .