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Differentiation is an operation in calculus used to find the rate of change of a function with respect to a variable. In simple terms, it gives us the slope of the function at any given point. The derivative of a function f(x) is denoted by f'(x) or \frac{d}{dx}f(x) and represents the rate of change of f(x) with respect to x.

Integration is another operation in calculus that is essentially the opposite of differentiation. It is used to determine the accumulation of a value over an interval. In simple terms, it gives us the area under the curve of a function. The integral of a function f(x) is denoted by \int f(x) dx and represents the accumulated value of f(x) over a specified interval.

The first part of the Fundamental Theorem of Calculus states that if a function F(x) is an antiderivative of f(x) (F'(x) = f(x)) on an interval [a,b], then the definite integral of f(x) on the interval [a,b], denoted by \int_a^b f(x) dx, can be calculated as F(b) - F(a). In other words, the definite integral of the function f(x) is equal to the difference in the values of its antiderivative, evaluated at the endpoints of the interval [a,b].

The inverse relationship between differentiation and integration is given by the fact that differentiation and integration are essentially opposite operations. When we differentiate a function, we find its rate of change, and when we integrate, we determine the accumulation of values over an interval. The Fundamental Theorem of Calculus links these concepts by formally stating that the definite integral of a function's derivative returns the original function up to a constant (assuming, of course, that the function is continuous and differentiable). This inverse relationship can be expressed as: \int_a^b \frac{d}{dx}F(x) dx = F(b) - F(a) In this expression, the definite integral of the derivative of F(x) is equal to the difference in the values of F(x) at the endpoints of the interval [a,b]. This demonstrates the inverse relationship between differentiation and integration as given by Part 1 of the Fundamental Theorem of Calculus.