Find the antiderivative of the function \(f(x) = 3x^2 - 5x + 7\).

Step 1 ：The antiderivative of a function is found by reversing the process of differentiation. For the function \(f(x) = 3x^2 - 5x + 7\), we need to find a function \(F(x)\) such that \(F'(x) = f(x)\).

Step 2 ：The antiderivative of \(3x^2\) is \(x^3\) because the derivative of \(x^3\) is \(3x^2\).

Step 3 ：The antiderivative of \(-5x\) is \(-\frac{5}{2}x^2\) because the derivative of \(-\frac{5}{2}x^2\) is \(-5x\).

Step 4 ：The antiderivative of \(7\) is \(7x\) because the derivative of \(7x\) is \(7\).

Step 5 ：Therefore, the antiderivative of \(f(x) = 3x^2 - 5x + 7\) is \(F(x) = x^3 -\frac{5}{2}x^2 + 7x + C\), where \(C\) is the constant of integration.