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April was asked to determine whether $f(x)=x^{3}-1$ is even, odd, or neither. Here is her work:$\newline$Step $1$: Find expression for $f(-x)$$\newline$$$\begin{aligned} f(-x) & =(-x)^{3}-1 \\ & =-x^{3}-1 \end{aligned}$$$\newline$Step $2$: Check if $f(-x)$ is equal to $f(x)$ or $-f(x)$$\newline$$-x^{3}-1$ is the same as$\newline$$-f(x)=-x^{3}-1$.$\newline$Step $3$: Conclusion$\newline$$f(-x)$ is equivalent to $-f(x)$, so $f$ is odd.$\newline$Is April's work correct? If not, what is the first step where April made a mistake?$\newline$Choose $1$ answer:$\newline$(A) April's work is correct.$\newline$(B) April's work is incorrect. She first made a mistake in Step $1$.$\newline$(C) April's work is incorrect. She first made a mistake in Step $2$.$\newline$(D) April's work is incorrect. She first made a mistake in Step $3$.