suppose f_n(x) is continues and periodic

suppose fn(x) converges to f(x) in L1(T) does f(x) has to be continues

??

how i tried:

||fn-f||_{L1(T)} is an integral from -pi to pi on |fn-f|

i know that if there is a finite number of discontinuety points in a function ,then the integral over it will be the same as a continues function

so i dont know

if its true or nor