I have been set the following question.

Show that the operatorL[f](x) = INT(0,x) f(s) dx, 0<= x <=1 , is bounded from C0(0,1) into itself.

where INT(0,x) is the integral between 0 and x, and C0(0,1) is the space of continuous functions with no continuous derivatives on (0,1).

I know that to show this I must show there exists c>0 such that

llLxll <= cllxll for all x.

However I am having trouble actually showing this exists. any ideas?