The following function are continuous on (0,π):

The  function f(x) =tanx  is not defined at x=π2, so f  is not continuous on (0,π)  since, the function g(x)=xsin1x  is continuous on (0,π)  and  the integral function of a continuous function is continuous, therefore F(x)=∫0xtsin1tdt  is continuous on (0,π) .For the function  f(x)=1, 0