Find the integral of f(x)= x^3 + 2x^2 + 1

Let's work our way from left to right. Starting with the x³ term we will take the integral with respect to x. First we add one to the power we get x⁴, next we take the coefficient and divide it by the new exponent leaving us with 1/4. Therefore our first term is (1/4)x⁴ . Moving on we take 2x² and add one to the power making x³. Take the coefficient and divide it by the new exponent getting 2/3. Our second term is then (2/3)x³. With the last term we have an exponent of 0 because x⁰=1. Add one to the exponent to get x¹ and divide the coefficient by the new exponent. The last term becomes x. The integral of f(x) is (1/4)x² + (2/3)x³ + x + C. Since this is an indefinite integral (meaning we have no limits) we leave C to be any constant. 

You can check your answer by taking the derivative of what you have to confirm it is the same as what the question gave for f(x).