If fff is a continuous function on [0,1][0, 1][0,1] and g(x)=∫0xf(t)dtg(x) = \int_0^x f(t) dtg(x)=∫0xf(t)dt, which of the following is true?
ggg is Lipschitz continuous.
ggg is not differentiable.
ggg is only continuous if fff is differentiable.
ggg must be zero.