APFIVE Particular Solution of a Differential Equation
If $$y=f(x)$$ is a solution to the differential equation $$\frac{dy}{dx}=e^{\sin(x)}$$ with the initial condition $$f(\frac{\pi}{2})=1$$, which of the following is true?
A
$$f(x)=e^{\sin(x)}$$
B
$$f(x)=\cos(x)e^{\sin(x)}$$
C
$$f(x)=1+\int_{\pi/2}^xe^{\sin(t)}\, dt$$
D
$$f(x)=1+\int_0^xe^{\sin(t)}\, dt$$
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