$w=a-b t=0$

$t=a / b$

$\theta=\int \omega d t=\int_{0}^{1}(a-b t) d t$

$=\left(a t-\frac{b t^{2}}{2}\right)_{0}^{a/b}$

$=a \cdot \frac{a}{b}-\frac{6}{2} \frac{a^{2}}{b^{2}}$

$=a^{2} / 2 b$