An antiderivative F(x) with F'(x)=f(x) F'(x)=f(x) f(x)=2x Now we take integration int F'(x)dx= int f(x) dx F(x)= int 2xdx F(x)=x^(2)+c Where c is a constant. Now find out integration constant by using given initial condition F(0)=0 F(0)=(0)^(2)+c 0=c Thus antiderivative become F(x)=x^(2) hence it is only one possible solution for given initial condition F(0)=0 Result: An antiderivative is F(x) is x^(2) with given initial condition F(0)=0