APFIVE Particular Solution as a Definite Integral
The function $$y=h(x)$$ is the solution to the differential equation $$\frac{dy}{dx}=\sin(x^2)$$ satisfying the initial condition $$h(1)=3$$. Which of the following is an expression for $$h(x)$$?
A
$$h(x)=3+\int_0^x\sin(t^2)\, dt$$
B
$$h(x)=-\cos(x^2)+C$$
C
$$h(x)=3+2x\cos(x^2)$$
D
$$h(x)=3+\int_1^x\sin(t^2)\, dt$$
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