Is the sentence true or false?

If a function f has a primitive function F on interval I, then f possesses the Darboux property on interval I. 

 Fill in the blank:

Every ____________function has a primitive.

Can a discontinuous function have a primitive function?

Is the sentence true or false?

All continuous functions have antiderivatives.

Is the sentence true or false?

The function f(x) = (sin 1/x, x ≠ 0, 5, x = 0 ) has a primitive

Is the sentence true or false?

Every discontinuous function has a primitive.

Is the sentence true or false?

The function f(x) = (2x cos1/x, x ≠ 0, 0, x = 0)  has a primitive

Is the sentence true or false?

The function f(x)=(sin1/x, x ≠ 0 , 0, x = 0) has a primitive

Is the sentence true or false?

Function sgn : R → R, defined as sgn(x) = −1 for x < 0, sgn(0) = 0 and sgn(x) = 1 for x > 0 has a primitive function on R.

Is the sentence true or false?

The function f(x) =( 0, x ≤ 0, 1, x > 0) has a primitive