Help me to solve this following problem. Thanks a lot.
"Let f(x) is a continuous function f:[0,1]\to [0,+\infty). Put g(x)=1+2\int_0^x f(x). Assume that g(x)\ge (f(x))^2 \forall x\in[0,1] . Prove that g(x)\le (1+x)^2"