Evaluate the indefinite integral $\int x^{2}dx$.

Solution

1. The power rule for integration states that $\int x^{n}dx=\frac{x^{n+1}}{n+1}+C$ for $n\ne -1$.
2. Applying this rule with $n=2$, we get $\int x^{2}dx=\frac{x^{2+1}}{2+1}+C$.
3. Simplifying the expression gives $\frac{x^3}{3}+C$.
4. Hence the answer is (A).