Sure, I'd be happy to explain!

Integration is a fundamental concept in calculus that involves finding the antiderivative of a function. The antiderivative of a function is another function that, when differentiated, gives the original function back. The process of finding the antiderivative is called integration.

To integrate a function, we use a set of rules and techniques. Some of the basic rules of integration include:

1. Power Rule: If f(x) = x^n, then the antiderivative of f(x) with respect to x is F(x) = (1/(n+1))x^(n+1) + C, where C is the constant of integration.

2. Sum/Difference Rule: If f(x) and g(x) are two functions, then the antiderivative of f(x) + g(x) with respect to x is the sum of the antiderivatives of f(x) and g(x).

3. Constant Multiple Rule: If c is a constant and f(x) is a function, then the antiderivative of c*f(x) with respect to x is c times the antiderivative of f(x) with respect to x.

Using the power rule, we can find the antiderivative of 5x^2 as follows:

f(x) = 5x^2
F(x) = ∫ f(x) dx
F(x) = ∫ 5x^2 dx
F(x) = (5/3)x^3 + C

So the antiderivative of 5x^2 is (5/3)x^3 + C, where C is the constant of integration.
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