Answer
${\bf 0.071 }\;\rm T\cdot m $
Work Step by Step
We can see that the magnetic field is in the same direction as the path.
So, the integral of $\vec B$ between the two points $i$ and $f$ is given by
$$\int_i^f \vec Bd\vec r=B r$$
where $r=\sqrt{x_f^2+y_f^2}$
$$\int_i^f \vec Bd\vec r=B \sqrt{x_f^2+y_f^2}$$
Plug the known from the given graph;
$$\int_i^f \vec Bd\vec r=0.10 \sqrt{0.5^2+0.5^2}=\color{red}{\bf 0.071 }\;\rm T\cdot m $$
