If I = $\int$ C $( \ln x + 2 ) d x + \left( e ^ { y } + 2 x \right) d y$

Multiple Choice

If I = $\int$ C $( \ln x + 2 ) d x + \left( e ^ { y } + 2 x \right) d y$ is independent of the path where C is a curve from (3, 1) to (1, 3) , then I is

A) $e ^ { 3 } + e + 3 \ln 3 + 6$
B) $e ^ { 3 } - e - 3 \ln 3 - 6$
C) $e ^ { 3 } - e + 3 \ln 3 + 6$
D) $e ^ { 3 } - e - 3 \ln 3 + 6$
E) $e ^ { 3 } + e - 3 \ln 3 + 6$