The figure shows the angular velocity versus time graph of a flywheel. The angle (in radians) through which the flywheel turns during 25 s is

Angle rotated, $\theta$ = Area under $\omega$-t graph.
Area under $\omega$-t graph = Area of trapezium OABCO

$\because \text{ Area of }(\square OABCO)=\frac{1}{2}\left(\text{ Sum of parallel sides }\right)\times \text{ Distance }$between them

$=\frac{1}{2}(AB+OC)\times AD=\frac{1}{2}(15+25)\times 30=600\mathrm{rad}$