solve f(4/5)=Integral(0 to 1) e^-2x dx

Hello!
Unfortunately, your question contains an unknown function f, and it is present only at the left part of the equation with the value 4/5 as an argument. We can find this number f(4/5), but not the function f itself.
With this in mind, compute the integral from the right part:
int_0^1 e^(-2x) dx = |t = - 2 x, t\in [0, -2], x = - 1 / 2 t, dx = - 1 / 2 dt| =

= int_0^(-2) e^t (- 1 / 2) dt = 1 / 2 int_(-2)^0 e^t dt = 1 / 2 e^t|_(t = -2)^0 = 1 / 2(e^0 - e^(-2)) = 1/2(1 - 1/e^2) approx -0.432.
We used a simple substitution t=-2x and the fact that int_a^b g(t) dt = -int_b^a g(t) dt.
So we know that f(4/5) =1/2(1-1/e^2) but know nothing more about the function f.
Please tell me if there was some error in the conditions, and I will update the solution.