What is the value of $\int_{-2}^3\min\{1,x^2\}dx$ I have another question:
What is the value of $$\int_{-2}^3\min\{1,x^2\}dx$$
Thanks your help!

$x^2 <1 \Rightarrow |x| < 1$. Therefore
$$\int^3_{-2}\min\{1,x^2\}\,dx = \int^{-1}_{-2}1\, dx + \int^{1}_{-1}x^2\,dx + \int^{3}_{1}1\,dx$$
