Explain why the function defined by F(x)=y_0+ _ a ^ x f(t) ,dt necessarily satisfies…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Explain why the function defined by

F(x)=y_0+\int_{a}^{x}f(t)\,dt

necessarily satisfies both the differential equation

\dfrac{dF}{dx}=f(x)

and the initial condition

F(a)=y_0

. Your answer should refer to one calculus theorem that justifies the result.