Find a function from a given derivative

[notweNcaasI]

Homework Statement

Find a function F such that F(2) = 0 and F'(x) = sin(e^x)

I think that this a reverse to Part 2 of the Fundamental Theorem of Calc but not really sure.

Homework Equations

From the Theorem:
A(x) = $$\int f(t) dt$$

A'(x) = f(x)

f(t) = sin(e^x) ??

∫

The Attempt at a Solution

I attempt to integrate sin(e^x) but that seems like a lost cause.

According to FTC II, the area function with lower limit a=2 is an antiderivative satisfying
F(2) = 0

F(x) = $$\int^{x}_{2} sin(e^t)dt$$

Is this the correct function

 

[Dick]

That works fine.