Solving integral with Fubini's theorem

Question

I have to solve $\int_0^1 y^7 e^{xy^4} \mathrm{d}y$ by using Fubini's theorem. My idea was to rewrite $y^7 e^{xy^4}$ as $\int_0^x f(t) \mathrm{d}t$, but I cannot figure out the term for $f$. I currently have $\int_0^x y^{11} e^{ty^4} \mathrm{d}t = y^7e^{xy^4}-y^7$.