Remember that integration is the opposite of differentiation. It's also known as the "antiderivative"
If f(x) = x^3 + 4x, the derivative is 3x^2 + 4
When integrating you will get x^3 + 4x + C
This is how it's done
Take 1 over (exponent +1) times the variable raised to the (n+1) power. Do this for each term
Thus we get 3(1/3)x^(2+1) + 4/1(x)^(0 + 1)
= x^3 + 4x
We add a C due to a constant of differentiation