And you can verify that this derivative is equal to sine of pi x. So the antiderivative of sine of pi x is this. The antiderivative of negative 8x to the third power is negative 8. I'm going to divide it by 4, so negative 2x to the fourth power. And all I did is I incremented the 3 to a 4, and then I divided the 8 by the 4. And you could take the derivative of this to verify that it is the same thing as negative 8x to the third power. And we're going to have to evaluate that from 0 to 1 half.