Find the integral. \[ \int\left(x^{2}-3 x+5\right) d x \]

Step 1 ：We are given the function \(f(x) = x^{2}-3 x+5\). We are asked to find the integral of this function.

Step 2 ：The integral of a function is the area under the curve of the function. The integral of a polynomial function can be found by applying the power rule for integration, which states that the integral of \(x^n dx\) is \(\frac{1}{n+1}x^{n+1}\).

Step 3 ：In this case, we have a polynomial of degree 2, so we can apply the power rule to each term separately. The integral of \(x^2\) is \(\frac{1}{3}x^{3}\), the integral of \(-3x\) is \(-\frac{3}{2}x^{2}\), and the integral of 5 is \(5x\).

Step 4 ：We also need to add a constant of integration, \(C\), to account for the fact that the antiderivative is not unique.

Step 5 ：Combining all these, the integral of \(x^{2}-3 x+5\) with respect to \(x\) is \(\frac{1}{3}x^{3} - \frac{3}{2}x^{2} + 5x + C\), where \(C\) is the constant of integration.

Step 6 ：\(\boxed{\frac{1}{3}x^{3} - \frac{3}{2}x^{2} + 5x + C}\) is the final answer.