Conditional mean: E(Y|x)

Question

Please help.I am not sure with my answer.Anyways, the problem goes this way: Find the conditional mean of $Y$ given $X=x$ ,$E(Y|x)$, if X and Y have the joint pdf of $f(x,y)=21x^2y^3, 0<x<y<1$, zero elsewhere.

Here is my solution: $$E(Y|x)=\int_x^1 y\ f_{y|x}(y) dy= \frac45\frac{(1-x)}{(1-x^4)}$$ where $$f_{y|x}(y)=\frac{f(x,y)}{f_x(x)}= \frac{4y^3}{(1-x^4)} $$and $$f_x(x)=\int_x^y 21x^2y^3dy$$