What is $\frac{d}{dx}\int_x^{x^2} t\,dt$?

Explanation

1. 01

   $\frac{d}{dx}\int_{u(x)}^{v(x)} f(t)\,dt = f(v)v' - f(u)u'$.

2. 02

   $= x^2 \cdot 2x - x \cdot 1 = 2x^3 - x$.