1. ## Trig Integrals

can I have some help with this problem:

integrate x^2 sin x^3 dx from 0 to 1

although I do not know that it equals 0.153233, that just what wolfram says

the integral should equal:

but now I am not sure how to use the 'from 0 to 1' in this. I thought that it would be something like:

We may substitute $u = x^3$, in which $du = 3x^2 dx \Rightarrow \frac{1}{3}du = x^2 dx$. You should be able to substitute and evaluate the new integral. Remember to back-substitute and then substitute the bounds.