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.

Put $F(x) = \displaystyle \int_{a}^x f(t)dt=x^2-2x-3$. Since $F(a) = 0$, $a^2-2a-3 = 0 \implies (a-1)^2 = 4\implies a - 1 = \pm 2 \implies a = -1, 3$. Thus there are $2$ answers: $a = -1,3$.
