Partial derivatives a function

I need to find the partial derivative of the function:

$$F(a,b) = \int_a^b\sqrt{t^3+1}\, \mathrm{d}t.$$

I can figure out how to get the partial derivative but I'm not sure how to simplify the function from a to b. How can I integrate this function?

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Simply use the fundamental theorem of calculus. You do not need to integrate. – 1015 Feb 15 '13 at 22:04

Hint: If $$G(t)=\int\sqrt{t^3+1}\,\mathrm{d}t$$ then $$\int_a^b\sqrt{t^3+1}\,\mathrm{d}t=G(b)-G(a)$$