If `f(x)=int_(x^(2))^(x^(2)+1)e^(-t^(2))dt` , then find the interval in which `f(x)` increases.

Explanation

To find the interval in which the function \( f(x) = \int_{x^2}^{x^2 + 1} e^{-t^2} dt \) increases, we need to follow these steps:

### Step 1: Differentiate \( f(x) \)
To determine where \( f(x) \) is increasing, we first need to find its derivative \( f'(x) \). We will use Leibniz's rule for differentiating under the integral sign.

\[ f'(x) = \frac{d}{dx} \left( \int_{x^2}^{x^2 + 1} e^{-t^2} dt \right) \]
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