In Order to Be Assured by a Theorem That the Fourier

In order to be assured by a theorem that the Fourier Series of $f$ on $[ a , b ]$ converges at $x$ , to $( f ( x + ) + f ( x - ) ) / 2$ which of the following conditions need to be satisfied? Select all that apply.

A) $f$ is continuous on $[ a , b ]$
B) $f ^ { \prime }$ is continuous on $[ a , b ]$
C) $f$ is piecewise continuous on $[ a , b ]$
D) $f ^ { \prime }$ is piecewise continuous on $[ a , b ]$
E) $f$ is integrable on $[ a , b ]$