Answer
$W=\dfrac{7}{3}+\dfrac{e^2-e}{2}$
Work Step by Step
Work done: $W=\int_C F\cdot dr=\int_0^{1} (y^2+1)^2(2y dy)+ye^{y^2+1} dy$
or, $=\int_0^{1} 2y (y^2+1)^2+ye^{y^2+1} dy$
Plug $y^2+1=k \implies 2y dy =dk$
Work done: $W=\int_C F\cdot dr=\int_1^2 k^2+\dfrac{e^k}{2} dk$
or, $=[\dfrac{k^3}{3}+\dfrac{e^k}{2}]_1^{2}$
or, $=[\dfrac{2^3}{3}+\dfrac{e^2}{2}]-[\dfrac{1^3}{3}+\dfrac{e^1}{2}]$
Hence,
Work done, $W=\dfrac{7}{3}+\dfrac{e^2-e}{2}$
