The function f(x)=tanx is not defined at x=2π​, so f(x) is not continuous on (0,π).(b) Since, g(x)=xsinx1​ is continuous on (0,π) and the integral function of a continuous function is continuous,∴f(x)=∫0x​t(sint1​)dt is continuous on (0,π).(c) Also, f(x)={1,2sin(92x​),​0