Find the integral. \[ \int\left(9 x^{2}-4 x+5\right) d x \] \[ \int\left(9 x^{2}-4 x+5\right) d x= \]

Step 1 ：The integral of a function is found by applying the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1), and the integral of a constant times a function is the constant times the integral of the function. The integral of a constant is the constant times x.

Step 2 ：So, to find the integral of the given function, we will apply the power rule to each term separately.

Step 3 ：The integral of the function \(9x^2 - 4x + 5\) is \(3x^3 - 2x^2 + 5x\). However, we must not forget to add the constant of integration, usually denoted as \(C\), to our answer. This is because the derivative of a constant is zero, so when we take the integral, we can't know what the original constant was, and we include \(C\) to account for this.

Step 4 ：Final Answer: \(\boxed{\int\left(9 x^{2}-4 x+5\right) d x = 3x^3 - 2x^2 + 5x + C}\)