Given definite integral is:

Let us assume ……(1)

Assume y = x²+1

Differentiating w.r.t x on both sides we get,

d(y) = d(x² + 1)

dy = 2x dx

……(2)

The upper limit for Integral

X = 4 ⇒ y = 4² + 1

Upper limit: y = 17……(3)

The lower limit for Integral

X = 2 ⇒ y = 2² + 1

Lower limit: y = 5 ……(4)

Substituting (2),(3),(4) in the eq(1), we get,

We know that:

We know that:

[here f’(x) is derivative of f(x))

We know that: