What is $\frac{d}{dx}\int_x^5 (t^3 + 1)\,dt$?

Explanation

1. 01

   $\int_x^5 f(t)\,dt = -\int_5^x f(t)\,dt$, and $\frac{d}{dx}\int_5^x f(t)\,dt = f(x)$.

2. 02

   So the derivative is $-(x^3 + 1)$.