How to solve $a$ in $\int_a^xf\left(t\right)dt=x^2-2x-3$ How do you solve for $a$ in $\int_a^xf\left(t\right)dt=x^2-2x-3$?
I have differentiated both sides with respect to $x$, but do not know how to continue after this.

$$F(x)-F(a)=x^2-2x-3\implies f(x)=2x-2$$
$$\int_a^xf\left(t\right)dt=[t^2-2t]_a^x=x^2-2x-a^2+2a$$
$$2a-a^2=-3\implies a^2-2a-3=0\implies a=1,-3$$
