Using the first fundamental theorem of calculus and the chain rule, find

Question

Using the first fundamental theorem of calculus and the chain rule, find

d/dx ∫^x₆ 2sin(t² + t + 5)dt

d/dx ∫^{sin^3(x)}_5x 2sin(t² + t + 5)dt

Answer 1

d/dx∫₆^x2sin(t²+ t + 5)dt = 2sin(x² + x + 5)

d/dx∫_5x^{sin^3(x)}2(t² + t + 5)dt = 2(sin⁶x + sin³x + 5)(3sin²xcosx) - 2(25x² + 5x + 5)(5)