Factor U Substitution

If u= $$x^2$$  and f(u)= $$u^3$$    then find $$\int_{ }^{ }f\left(u\right)du$$  as a function of u.

If u= $$x^2$$   and f(u)= $$u^3$$ then find $$\int_{ }^{ }f\left(u\right)du\$$  as a function of x this time.  

$$\int_{ }^{ }f\left(x\right)dx\ \ \ \ \ \ \int_{ }^{ }f\left(u\right)du\ \ \ \ \ \ \int_{ }^{ }f\left(x\right)du\ \ \ \ \ \int_{ }^{ }f\left(u\right)dx$$  

Let f(x)=x3+1 and u=x2, which of these are equivalent?