Composite function with integral

Question

Suppose $f(z)=\int_{0}^{z} g(y)dy, h(x)=x^2$, then the composite $f\circ h=\int_{0}^{x^2} g(y)dy$. Is this correct?

Answer 1

Yes that's right. $f \circ h = f(h(x))$ so you just plug in $h(x)$ for $z$ to get $\int_{0}^{x^2} g(y) dy$.

Answer 2

This is correct because $$f(h(x))=f(x^2)=\int_{0}^{x^2} g(y) dy. $$