Find the restricted space within function and line

Question

I have the following question:

Let $f(x)=x + sin(x)^2$ defined for every $-\pi\le x \le\pi$. Find the entire restricted space within the $f(x)$ and the line $y = x$.

I drew the intersecting graphs on paper and attempted to solve it using a derivative but I can't find out how to approach this question. I'd be thankful for advice about starting point and/or an explanation about this question.

Thanks!

Answer 1

You can find the solution by checking out the graphic representation of these two functions. Then you can just integrate:

$$\int_{-\pi}^0 x-(x+sin^2(x) )dx+\int_{0}^{\pi}x+sin^2(x)-x dx$$

do you know how to solve these integrals?