A force F = 20 + 10y acts on a particle in y -direction where F is...

Work done is calculated by taking the dot product between the force and the displacement.

$W = ∫ F \cdot dy$
$= \mathop{∫}_{0}^{1}20\text{d}y + \mathop{∫}_{0}^{1}10ydy$
$= {\left[20y\right]}_{0}^{1} + 5{\left[{y}^{2}\right]}_{0}^{1}$
$= 20 + 5 = 25J$