note …
[math]\int_{x^3}^{10} \sqrt{t^6 +1} \, dt = -\int_{10}^{x^3} \sqrt{t^6+1} \, dt[/math]
also, if [imath]a[/imath] is a constant and [imath]u[/imath] is a function of [imath]x[/imath] …
[math]\dfrac{d}{dx} \bigg[-\int_a^u f(t) \, dt \bigg] = -f(u) \cdot \dfrac{du}{dx}[/math]