This means we need to solve the equation:
\[
\int_0^1 f(x) \, dx = 1.
\]
Substituting the given density function, we have:
\[
\int_0^1 (a + b x^2) \, dx = 1.
\]
Step 2:
Now, we compute the integral:
\[
\int_0^1 (a + b x^2) \, dx = \int_0^1 a \, dx + \int_0^1 b
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