I need to solve the following
$$\min_{c,d} \int_0^1 |ct+d-t^2| dt.$$
Since the integrand is of degree two, I considered to split the integral in three. My problem however, is that the bounds would then depend on $c$ as well as $d$. Is there any extension of the Leibnitz integral rule (https://en.wikipedia.org/wiki/Leibniz_integral_rule) that lets you deal with two parameters in the bound?