Find a Function $f$ Such That $\mathbf { F } = \nabla f$

Short Answer

Find a function $f$ such that $\mathbf { F } = \nabla f$ and use it to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the given curve $C$ .
$$\mathbf { F } ( x , y ) = y \mathbf { i } + ( x + 10 y ) \mathbf { j }$$
$C$ is the upper semicircle that starts at $( 1,2 )$ and ends at $( 5,2 )$ .