Fn(x)=|Sin^n(X)| is convergent to F(x) where F(x) =1 when x=(m+1/2)pi and F(x) =0when x =otherwise

prove integrate from -infinity to +ve infinity

1. not sure how to integrate a function that is discontinuous at a single point

2 my main confusion is Lim n->inf Fn(x) = 0 which is equal to F(x). Intuitively I can tell the area under sin^n X is not zero even when n->infinity. but I am not sure how to prove it using mathematical formulae