b
\(\mathrm{W}=\int_{\vec{r_i}}^{\vec{r_g}} \overrightarrow{\mathrm{F}} \cdot \mathrm{d} \overrightarrow{\mathrm{r}}\)

\(\mathrm{W}=\int_{1}^{0}-\mathrm{x} \mathrm{d} \mathrm{x}+\int_{0}^{1} \mathrm{ydy}\)

\(W=\left.\frac{-x^{2}}{2}\right|_{1} ^{0}+\left.\frac{y^{2}}{2}\right|_{0} ^{1}\)

\(=-\left(\frac{0^{2}}{2}-\frac{1^{2}}{2}\right)+\left(\frac{1^{2}}{2}-\frac{0^{2}}{2}\right)\)

\(\mathrm{W}=1 \mathrm{J}\)